Question: This gets described as a reboot rather than a sequel, but why? Nothing directly contradicts the original, as far as I'm aware, the only real change is the title character being recast - hardly unusual for a franchise.
Question: In the scene where they cross the bridge with the train, and Allison French is being held by those two guys with a rope around her neck, so that if they would shoot the guys, the horse would run off and break her neck, suffocate her or whatever... They were with 4 against 2, so why didn't one of 'em just shoot that horse?
Answer: There's no explanation. It could be that no one thought of this. Also, even if they shot the horse, the girl could still be injured or killed. If the horse was only wounded, it could have bolted, reared up, or fallen and then rolled on top of the girl. There's many different scenarios that could have played out.
Chosen answer: I haven't seen this movie in several years, but one contradiction I distinctly remember is the Punisher having a deceased daughter in this film, whereas in the 2004 film, he only had a son. The 2004 film had the Punisher's wife and son (named Will here) murdered in Puerto Rico and buried and Tampa. This film takes place in New York, and the cemetery the Punisher goes to has a gravestone for his wife, daughter and son (named Frank, Jr. here). There is also a brief flashback in this scene of the Punisher sitting on a picnic blanket with his dead family around him, which is closer to the comics origin where his family were collateral damage in a gang crossfire. The 2004 film depicted his family as being the deliberate targets of a mob hit and were run over by a truck on a pier.
Phaneron ★