How could Andy Dufresne do so much after his escape without being caught?

You're forgetting a few important points;

• Andy Dufresne escaped Shawshank in 1966 - around this time many of the modern security measures in place in the banking industry did not exist
• Andy Dufresne had all of the valid identification and signatures, matching up with the account holders, as he had set up the accounts
• Banks open at around 8am
• he also ask for cashier’s check not cash
• Let's not forget, Andy was an exceptionally intelligent banker, he knew exactly what he needed to say in order to withdraw the contents of each of these accounts with the least amount of friction
• Considering his intelligence, it makes sense he would have planned which order to visit each bank, to ensure that he went to the closest ones first and travelled out to the furthest one last
• If you consider that lights on had been at 8am, there was a 30-60 minute period while the warden investigated how he had escaped, it would have taken the prison guards at least another hour or so to follow Andy's route out of prison, and in the scene where the guards and dogs are following the sewage route out of the prison, the sun is high in the sky
• Andy would have purchased the car with cash, and again many of the fraud methods used today did not exist back then

Now, in regards to Andy acting out in the open - CCTV wasn't around back then, the only way the banks would have known is if the police had been in with a picture. Considering the timeframe highlighted above of "several hours" - Andy would have already been in the car by this point. By the time Andy has got in the convertible, he is going to be uncatchable short of some very bad luck. He heads out into a field in the middle of nowhere to hide his cache for Red to later find, and then heads off to Mexico, which is outside of the jurisdiction of the USA.

I believe there was enough time for Andy to have completed his tasks.

Consider this:

• Andy misses roll call and the guard discovers his cell is empty.
• At the same time the Warden discovers Andy left his old shoes in the shoe box.
• The warden travels down and discovers Andy is the one missing. He orders everyone on the cell block questioned, starting with Red.
• The warden orders Hadley to find him. Because Andy was in his cell the previous night they probably think he should be close by.
• A few minutes later they discover the hole in the wall.
• They had to take time to send someone in the hole to the sewer line, and then to either go through the sewer line (which Andy may still be in) or discover its outlet.

Considering the interviewing of the other prisoners, going through the escape route and the initial search of the surrounding area, I think it would be hours before they verified he wasn't in the area and they had to broaden their search. By the early afternoon Andy was likely leaving the state. Manhunts are slow. You establish some perceived parameter and then get people in lines walking all through it with dogs hoping to stumble upon the perp. It takes forever.

Additionally the warden didn't have any reason to think Andy would head to a bank, because he didn't discover Andy had stolen his ledgers until after Andy's story hit the papers.

Andy on the other hand had the following tasks that day.

• Sometime through the middle of the night he had to get cleaned up and walk to town.
• He had to go to a bank (presumably the closest one) to get cash.
• Then he would have likely bought the car, thus making it faster for him to hit all the other banks.
• Red says he visited nearly a dozen banks that morning. I guess either these banks were very close to each other and/or closing the accounts took less than 20 minutes on average per bank. That is pretty fast, but Andy was a banker, and probably knew just what to say to expedite the process.
• Buxton, Maine is only 15 miles from Portland, Maine. It would have only taken Andy 30 minutes to drive there and maybe 30-60 minutes to plant the box for Red.

From there Andy had to drive to Texas, which Google Maps estimates taking 36 hours on modern roads. In the 1960s it would have taken longer. Maybe 3-4 days. Because the police had no reason to suspect Andy had such vast resources, their initial search wouldn't have warranted a nationwide APB (if such a thing existed back then).

By the time they figured out what had happened Andy was probably several states away, and was able to cross the border a couple of days later.

He is no longer Andy Dufresne. He is now Randall Stevens. The only person who would know that name was the warden.

The warden also would not have informed the Police of the fraud he had been involved in, hence him comitting suicide.. Andy would have written to all of the banks before arriving to collect his loot and at the end of the day, he was able to do all this for one reason, pure and simply he is Andy Dufresne, not even Superman comes close.

Hmm... I assumed that Andy goes to the banks on the first day and asks them to add the ledger to their outgoing mail on the first day. Mail usually doesn't get to its destination the same day. Perhaps it is the following day if it is nearby. So it probably doesn't appear in the newspaper until the evening edition of the day after Andy escapes, or the morning edition two days later. (Remember, they show a newspaper after he escapes. So I would assume the newspapers detailing "corruption, murder at Shawshank" are 2-3 days after he escapes.) The police during that time probably had no reason to suspect that Andy has purchased a car and is a long ways away... And Warden Norton shot himself. We can assume that the police do not track the accounts of Randall Stevens until at least a day after that. Andy has at least a two day head start in his car, probably even longer... And in 1966 it certainly would have been much easier to pull off.

We also do not know what level of detail is in the ledgers. If I were him, why would want it known the the deposits went to accounts held by Randall Stevens? Is it theoretically possible he could have left this information out?

Your question is based upon some false premises. First of all, as pointed out by others, the Warden doesn't know, until days later, that the ledgers and documentation have been switched out. That includes the driver's license, birth certificate and social security card. There is no reason for anyone to suspect that Randall Stevens was suddenly walking around Maine.

Given that, regarding Dufresne's lack of hiding his identity - why would anyone be looking for a just-escaped convict as someone dressed in an expensive business suit at local banks? With matching signature, the ease, confidence and polish of a businessman, people are not going to assume "this guy is a hardened convict posing" even if they heard of the escape.

Why would he need advanced notice to close out the accounts? In the scene where he asks them to mail his package, his request is preceded by the bank teller saying, "Here is your cashier's check."

He could easily withdraw small sums of cash from all of the banks, or hit the biggest bank first and take out enough to get a car and spending money to get to Mexico. Remember, this is the mid-1960s. Cash transactions for car purchases were much more common then because of the smaller amounts. A new car would set you back under $2000. A used one? Considerably less. He could have taken $100 - $200 cash at each stop, and the rest as a bank draft with no eyebrows raised, and no need to insure cash reserves at any bank.

He was able to not get caught because only he and the warden knew of the network of accounts, only he knew he stole all the needed documentation, at that time, and no one would expect a convict to do anything but run away. He had the element of surprise.

Warden Norton did not appear to prioritize notifying authorities outside the prison

Norton is seen issuing instructions to his own officers to find Andy, but never making contact with the authorities outside the prison. He may have delayed, believing that by investigation he could track Andy down. He will also have been uneasy about what Andy would say to the police about Norton's malfeasance if they captured him.

Lack of Police Resources

An escape from prison, while embarrassing, may not have been the Police's top priority. Andy's conviction for murder was a crime of passion, making it unlikely that he would quickly re-offend. He is a convicted murderer, not a serial killer.

Andy's miraculous comportment

Having strategically stolen high-end clothing from Norton, Andy comports himself as a smart, well-to-do businessman. He retains his assured manner from his banking days. He also has an assumed name and excellent documentation. While the authorities will have been looking for a bedraggled and deskilled former inmate, Andy 'hides in plain sight' with his new identity.

The warden could also have delayed reporting the disappearance because if the search revealed that Andy had died while trying to escape, or if he was captured during the search, then the warden and his men could hush-up the whole thing and nobody on the outside would even know that there was an attempted escape. A prison escape, or even a failed attempt at escape, under his watch is probably not any warden would like to have on his own re'sume' !

Only when it became very clear that Andy had indeed escaped would the warden report it to the outside authorities. That might have taken a good 3 to 4 hours, perhaps even 6 to 8 hours and by that time, Andy would have been well on his way, and somewhere between Worcester, MA and Stamford, CT! At the very least, he would have been able to finish burying the letter at Buxton and departed from that place.