ESPN's Mike Reiss noted that the Patriots played tackles LaAdrian Waddle and Marcus Cannon as "the top two players at the position" at practice this week. The Patriots were without incumbent starters Nate Solder and Sebastian Vollmer.
Waddle was aligned on the left side, with Cannon on the right. This statement of usage reveals a lot about the Patriots tackle depth this season.
1) Tight end Michael Williams is remaining at tight end, and not moving to tackle. Waddle is also ahead of Cameron Fleming in the depth chart.
2) Patriots director of player personnel Nick Caserio has stated that Cannon is a better fit at right tackle than at left tackle or guard. It's easy to read into Cannon's placement on the right as a way to get him back to being a comfortable player on the line, and to get him settled after his disastrous stint at left tackle.
3) Waddle was historically a right tackle with the Lions, before the Patriots claimed him, but played left tackle for 37 snaps with the Patriots after Vollmer went down with an injury against the Jets; Waddle suffered an injury of his own before the game ended.
4) I theorize that Waddle is playing left tackle in practice as a way to both improve his versatility, and to allow Cannon to remain on the right side in hopes that Cannon can find his groove. Waddle was likely on the left side out of necessity (he would only play there if Solder, Vollmer, and Cannon were hurt) and not because he is the ideal back-up for Solder.
This lineup is more for Cannon than for anyone else, and not an indication that Waddle is ahead of Cannon on the depth chart.