The New England Patriots do not have an issue with their starting cornerbacks. I would even argue that the combination of Malcolm Butler and Logan Ryan would rank comfortably in the top 5-10 range when looking across the league. Without a doubt they are an above average duo.
They are not a weakness.
I would even say that undrafted rookie Justin Coleman isn't a weakness, although his wrist injury is certainly concerning and worth monitoring. Per NESN's Doug Kyed, Coleman actually breaks up more passes per target than Malcolm Butler, so hopefully Coleman recovers quickly.
With Butler, Ryan, and Coleman, the Patriots have a trio of cornerbacks that have a sense for the ball and are all worthy of seeing the field.
The issue comes if and when any of them are injured, like when Coleman was injured this past game. Injuries are an important factor with the cornerback position, and you don't have to look any further than the Patriots roster. Darryl Roberts was lost in the preseason. Tarell Brown is on the injured reserve. Bradley Fletcher was cut because of his play and his hamstring injury.
Rashaan Melvin is the team's current fourth corner, and Chris Greenwood has just been added to the practice squad. I'd argue that the secondary would be better off with Duron Harmon at free safety and Devin McCourty at cornerback, than with having Melvin in the secondary.
Luckily for the Patriots, this hole is less minor than others and it's only for the short term. Roberts is an extremely promising player, and a quartet of Butler, Ryan, Coleman, and Roberts moving forward would be fantastic- and a veteran like Brown could be the cherry on top.
But for the rest of the season, Patriots fans should watch the secondary with bated breath- not because they might give up a big play, but because any injury would put a serious damper on the defense's potential.