In the title sequence, what is the strange futuristic noise/blinking effect?

Its the sound made by the viewing lens changing. If you watch the intro carefully, you'll see that the "zoom" changes in conjunction with the sound. Apart from being a cool effect, I doubt it has any deeper meaning.

After the Season 6 Finale we also see that the orbs and rings we see in the opening are most likely an astrolabe (aka armillary sphere, armilla, or armil).

We see the same object hanging in the Citadel at Oldtown. This can be determined by seeing the same markings on the rings.

The meaning of this is still not fully known, but there is an interesting fan theory...

"The overarching saga is called A Song Of Ice And Fire after all, and in the world of Game of Thrones songs are used to pass on heroic stories and legends. So does that mean somebody is telling this story of Dany, Jon, Arya, Cersei, and the rest to future generations?"

"If that’s how it ends, some fans might be mad about the set up of the story. But if this theory is right, does it make sense for Sam to be the one that devotes his life to passing along the heroism and cruelty of everyone in Westeros? Or could it be Sam’s son who was told the story by his father and then passes it on to his own children? If this theory is accurate, there are any number of options that would make sense. But for now it is just another theory."

As for the "blinking effect" the fan theory is that this is literally a person blinking because that person is using the optical device we see the Maester at Oldtown using.

Opening astrolabe

Citadel astroslabe

I think it goes with the mechanical theme for the intro - when they change zoom level they accompany it with a 'snick' sound and show the edge of the new lens crossing the screen. To zoom in more there are multiple lenses to slide in, so multiple 'snicks'.

This is similar to how you change magnification level with a microscope. It's very hard to smoothly change zoom at small scales, and I think they want to reinforce the effect of the intro being a mechanical map that's just about possible using the technology available in the series.

In fact, from what I have seen, that blinking effect comes from the globe that shows up between the map shots at the scene. It keeps spinning during the whole opening, and its rings move making that blinking sound. In the internet, they call it the Astrolabe (had to link because the image is too big):

Game of Thrones Astrolabe

It seems to not have importance at all, but if you look closely and pause at certain parts, its design shows the animals of the families they represent (such as the dragon of Targaryen, the lion of Lannister, the stag of Baratheon and the wolf of Stark).

The picture below is a close-up of the astrolabe and it seems to hint at Robert's Rebellion:

As of the dragon (Aerys Targaryen) is being attacked from both sides by the wolf (Eddard Stark) and the stag (Robert Baratheon), and surprisingly being also held up from behind by the lion (Jaime Lannister, who betrays and kills him).

If you look on the internet, more shots like this can be seen throughout the opening, with a few more hints of the show's backstory. Everything seems to have a meaning on this, it is pretty amazing.