Too Many Characters/ Storylines
Gotham has thrown so many characters at the audience and has expected us to stay invested in all of them. The series often spends too much time on characters that are uninteresting. The cast is so large that it feels like the actors are fighting for screen time in some episodes. Is the protagonist Jim Gordan or Bruce Wayne? While a strong argument can be made for both them, it should be more distinct. Honestly I think if they made a story about Jim Gordan, and how a city like Gotham changed his views morally; his character progression would be more interesting than another Bruce Wayne origin story.
The Villains
Gotham is a prequel series that focuses on the city Pre-Batman. It is a little confusing as to why certain characters are appearing this early. Since (for the most part) Batman's antagonists are supposed to roughly be his age (However there are exceptions to this rule). When the show introduces all of these A-list Batman villains before Batman has even hit puberty is a bit ridiculous. I get that they have to keep it new and intersting every week, and keep the non comic readers in the loop with refrences or appearnces from popular villains. But there is no reason for Harvey Dent, Victor Fries, or Edward Nygma to be on the show yet. The show should work with what they have such as: Falcone Family, Maroni Family, Black Mask, Penguin, Hugo Strange, Selina Kyle (as a petty thief), etc. Or continue to introduce less popular villains that the GCPD can handle such as Calendar Man, Ventriliquist, Jervis Tetch, or Professor Pyg.
Another problem Gotham faces is villain overload. To eleaborate, the series will feature many villains in one-and-done type episodes. I'd rather have a single villain that is fleshed out, than multiple villains with rushed storylines.
Choose a Time Period
Though it is obvious Gotham is a prequel. It is unclear when exactly Gotham takes place. In Season 1 Episode 4 a variety of technological items are used that conflict with eachother. The use of typewriters along with 80's or 90's style computers and flip phones from the early 2000's are just a few examples (The vehicles used and the fashion of chracters is a whole other inconsistency in the timeline that deserves its own section.) . I assume the ambiguity is on purpose considering this happens constantly. It is sort of annoying though, and I wish they'd just make up their minds. A gritty cop drama set in the 70's or 80's would be ideal in my eyes.
Another good reason to choose a time period would be to reference events that have happened in that decade or year thus making the setting more believable .
No More Barbara Kean
I'll try to be brief, considering the fact that anyone who has ever watched Gotham will probably know where I'm coming from in this part. Barbara Kean is by far the weakest character on the show. The writers don't really know what to do with her and often times her character drags the show down.
Cartoony or Gritty?
Or
Throughout the seasons Gotham has faced an identity problem. It is the reason we have seen villains like the Balloonman and stellar villains like Jerome. The show doesn't know what it wants to be, tonally. Whether gritty or cartoony, the show's directors or writers need to decide. Personally I think the show works better as a dark gritty crime drama based on Batman's extensive lore.