Once Aaron Hernandez was arrested for murder the entire NFL had the chance to look back in hindsight at all the signs that were missed, but there were a few teams that could not get past his character issues while at the University of Florida, including the local state team in the Miami Dolphins.
According to Pro Football Talk, the Dolphins had Hernandez off of their draft board due to his issues in college in the 2010 draft and they weren't the only team. Bengals owner Mike Brown and Colts exec Bill Polian said that they too took him off the board and the Dolphins also confirmed that as sources told the Sun-Sentinel that he was not one of their options in the draft.
The article says that the team had issues with three incidents during his time in college, including in a shooting, a positive drug test for weed and one time when he punched a bar employee. With the bright lights of Miami behind them, the team felt Hernandez was not a fit. The teams that passed on him likely caught a break, but no one could have known that he could get accused of murder.
Now NFL teams will be even more careful when evaluating players, but if certain stars can translate into wins, NFL teams will likely overlook anything.