My first thought is yes, they do, but I wanted to ask and make sure.

Say a player is doing a thing, they have three dice in their pool and one of them is glitched. They roll a 6 on the glitched die and a 2 and a 6 on the other dice. My inclination is to say: that's two 6s, so that's a critical success, and then the glitched die being a 6 means they avoid another consequence--the best possible roll for our player.

I could see another GM saying that's just a 6 result, a complete but not critical success, and then a 6 on the glitched die, so the glitchy extra trouble was also dodged. Would I be correct, or would this hypothetical other GM be correct?

My reading of the rules is, yes, you are correct. The glitched die is still a regular die -- speaking to the fiction,  that's why you still use the glitchy resource the die represents:  it can still get you success, but it's an increased risk.

Correct, the GLITCH die counts towards the overall outcome of the roll. 

Another example: If you roll 2 regular dice and 1 Glitched die, the heighest being a 4 on the Glitched, you get a Consequence for the Partial (4) and an additional Consequence from the Glitched.

Thanks for the confirmations, Emanoel and ishldgetoutmore! Good to know I had it correct.