The Patriots are no stranger to the 32nd pick in the NFL draft, as they are often selecting there after winning the Super Bowl. While the 32nd pick usually doesn't have the same hype and promise as a top 10 pick, there have been some pretty significant guys taken at the last pick of the 1st round.
Drew Brees 2001
Drew Brees technically went first pick in the second round of the 2001 draft, but with there being only 31 teams at the time, the Chargers did actually take him at 32.
Logan Mankins 2005
The Pats selected guard Logan Mankins at 32 in the 2005 draft even though he was projected to be a mid-third rounder. Mankins had a very successful career in New England until his eventual trade to Tampa Bay before the 2014 season.
Ben Watson 2004
The Pats were picking again at 32 in 2004, and picked up tight end Ben Watson. Watson had a very productive career in New England, and then continued his success with the Saints.
These are just a few players picked at 32 in the draft, but it just goes to show that there is talent all throughout the draft, and teams just have to do their research and find them. Also on a side note, I would much rather be picking a player at 32 than 1, just saying.