What is the farthest we can see into the universe? Is there a limit in which the mass in space obscure the ability to detect anything farther even as technology progresses?

Related:


Can the range of the observable universe be extended through an intermediary?
Which galaxy is receding from the Milky Way the fastest? What is known of the mechanism behind its recession?
It depends. In some areas, far-away stuff is obscured by obstacles in the foreground. In other places, we can see almost all the way to the earliest (and furthest-away) galaxies, like in the Hubble Deep Field image: 



The very earliest objects have so much redshift they disappear out of view for visible-light telescopes. That's where the JWST comes in: because it's an infrared telescope, it can capture objects that have too much redshift to be visible in a visible-light telescope. 

Advances help us see more in other ways too. Gaia data revealed some small nearby galaxies which are mostly obscured by our own galaxy.