Factual error: After the scene where Frank Castle steals the bus to rescue the children, the mobsters are firing at the bus. Not one bullet pierces a hole in the bus. Who knew Public Transit was bullet proof?
Visible crew/equipment: When The Punisher is being tortured on the 'rack', look on the floor. You can see the tape on the floor for 'blocking' the actors. Some of them actually stand where they are supposed to.
Factual error: After The Punisher rescues Tommy from his cell, they run to get Kathy. When they find her, Tommy says "Come on outside to the bus Kathy". However, there is no way for Tommy to know that The Punisher had brought the bus. (00:54:20)
Continuity mistake: In an earlier scene when The Punisher is at the mobster's house and the house gets set on fire, he is standing in the doorway killing bad guys. One second he is in the doorway and the next he is standing firmly on the ground.
Visible crew/equipment: When Jake and Sam first enter the sewer you can see a cameraman's feet and legs at the bottom right, and see his shadow as he runs into the tunnel. (00:47:40 - 00:48:10)
Continuity mistake: Lady Tanaka's daughter's earrings are removed during her fight with the Punisher, but they're back on her ears after she's sliced his arms with them then they're gone again. (01:40:16 - 01:44:46)
Answer: With how many criminals Frank has killed, many of them would definitely want revenge. By hiding in the sewers, there's less chance of him or his hideout being discovered. If Frank lived anywhere above ground, his enemies would be able to find him more quickly and kill him.