For the BB era, it is tough to top that no-talent JAG Jordan Richards. All the other questionable/terrible 1st and 2nd round picks from the past 20 years at least had one - or several - elite physical tools. Richards had exactly zero.
But the worst Patriots pick in my football-watching lifetime came in round 1 of the 1992 draft, where Joe Mendes put on an absolute clinic in how to mismanage a draft. These were lean times for the team, when the club routinely used their top draft picks on "need" rather than BPA.
Pats had the 8th pick in Rounds 1 and 2 (#8 and #37 overall). The consensus going into the draft was that they "needed" a LT in round 1. There were 3 LTs with a Round 1 grade in 1992 - Bob Whitfield and Leon Searcy, who were both rated in the top 15, if not the top 10, and Eugene Chung, who carried a mid to late first round grade.
Pick 8 comes up and all 3 LTs are available. As we learned after the draft, the Pats top choice among the 3 was Searcy. Atlanta calls and they are hot after Whitfield. But they are all the way back at 19. The Pats figure that they can extract a haul of picks from Atlanta and still get Searcy at 19 because Mendes figures that none of the other teams between 8 and 19 "need" a OT. And, worst case, even if someone surprisingly takes Searcy, Chung is pretty much guaranteed to be there at 19 as a fall back to allow the team to get the LT they think they need.
So the Pats pull the trigger on Atlanta trade and pick up a mid-second (#46 overall) and mid-4th along with pick #19. The Falcons take Whitfield at 8 as expected. But then Pittsburgh swoops in and grabs Searcy at 11. The Patriots suddenly decide to panic (what if we lose out now on Chung??) and start calling teams to trade back UP in the 1st round. Unfortunately, the Cowboys - on the cusp of the start of their 1990s dynasty - are sitting at #13 and smell blood in the water. They take back the 19th pick and the 4th rounder the Pats just acquired from Atlanta and get the Pats to throw in their OWN second round pick (#37).
Pats then get Chung at #13 (hooray), who does his best Sale Isaia impression in Foxboro for a few seasons until he is left unprotected to Jacksonville in the 1995 expansion draft. Whitfield and Searcy both go on to have solid careers. The Cowboys take Darren Woodson with the second rounder they stole from Mendes, who ends up having a pretty good career himself.
So for the low quality of the player relative to where he was picked in the draft and the ridiculous contortions the Pats went through to be in a position to draft said player (while sabotaging themselves from getting the player they really wanted and who was there at #8 for the taking), my vote for the worst Patriots draft pick of my NFL-watching lifetime goes to EUGENE CHUNG.