Anna seems to be a bit of a Faux Action Girl but if you think about it, she's a woman in Victorian society so it's likely the men in her family did most of the fighting and Anna was most likely trained to defend herself but not given as many opportunities to do so. Most likely she started fighting full time when her father disappeared but she still had her brother to help her. It makes her Moment of Awesome where she stakes Aleera that much better.
The Valerious family made a vow that they would never rest and enter Heaven until Dracula is dead. This is actually applied literally, which many of them misunderstand, believing they must be the ones to finally kill him. This is not actually the case. If Anna dies before Dracula, the curse still will be lifted if he were slain later by another... because the last Valerious would actually be Dracula himself. He was the son of the Valerious who initially made the vow, thus his death would still allow the family to rest as the vow would now be applicable to him as the only Valerious left to fufill it. Although this is never touched on in the movie because Werewolf!Van Helsing had already killed Dracula by the time Anna died, it's likely there was never any race to defeat Dracula before Anna and Velkan died.
Igor turns out to be The Renfield to Dracula. In the original movies, Renfield and Fritz (the character mistakenly called Igor) were both played by the same actor, Dwight Frye.
Perhaps the original deal wasn't quite what it sounds like. Perhaps it was a kind of "Sold Your Soul To God" thing? Perhaps the deal was that once Dracula had been killed with the assistance of a Valerious, every member of the family would go to Heaven, regardless of their actions in life, just as a deal with the Devil might see you going to Hell. In the bible itself Jesus wasn't adverse to making deals in exchange for suffering (such as with James and John). Such a deal would indeed have risks in the light of failure.
Dracula's extreme hamminess actually makes a lot of sense given his rant about feeling nothing. All of his bombast and shows of false emotion are him trying to portray what he thinks he should be feeling in any given situation.
Why is Van Helsing have such terrible aim with the repeating crossbow, despite being a crack shot with pistols during his fight with Mr Hyde? It's because Van Helsing had no time to train with the new weapon (it's, at most, a few weeks between receiving the crossbow and arriving in the village, and most of that time would have been spent traveling), nor would he have experience with any similar weapon (this is an era before assault rifles or machine guns were commonplace on the battlefield). He basically got handed an experimental prototype and told to field test it.
During the masquerade ball, there's at one point a shot of Dracula and Anna in front of the mirror. Of course, Dracula is invisible and Anna is visible. However, they aren't alone and, realistically, the guests near them and behind them should also appear in the mirror, yet they don't. This of course foreshadows the reveal that everyone in the palace is a vampire.
Dracula is the son of Valerious, one of Anna's ancestors, which means they are related. Some viewers might be uncomfortable with him deciding to make her his bride (including, presumably, having his brood) with that in mind, even if they wouldn't really have much in common genetically given the large generational gap.