There are several things you can try to improve your experience with this game. That said, they all come with one big caveat: Do not approach this by telling your GM that he's "doing it wrong". There are a lot of different styles of GMing and playing, and even if the GM is using one that you personally don't like, that doesn't mean it's wrong or objectively unenjoyable. Perhaps the GM doesn't find plot-heavy campaigns fun, or he knows other players in the group don't. Perhaps he comes from a background of combat-heavy games where plot was never an issue. Perhaps he's used to games where the player roster isn't consistent enough to support plot. Whatever the case, he's the GM and he's not doing anything "wrong" any more than you are playing "wrong" by wanting more plot.
Consider a few things before deciding how you want to approach the issue:
Do the other players like the current game?
If the other players are enjoying the game as-is, then you've simply got a playstyle mismatch. What you find fun in an RPG isn't the same as what your friends find fun. Again, there's nothing inherently wrong with this; it just means that you're not likely to enjoy playing (this style of) games with them. If you're the only one who's not happy with the game as it's being run, then you have two choices: accept the style and don't expect your actions to affect the world, or leave the game. Which one you pick depends on you and your friends - how much do you enjoy the time hanging out with them independently of your enjoyment of the game? Do you have other things you can do with them so that the loss of the game won't affect your relationship? Are you so frustrated with the game that your annoyance is leaking from the game to your friends? Etc.
Does the GM like the current game, but the other players don't?
If the other players are as dissatisfied with the game as you are, then you should talk to your GM as a group, either before or after a game. Highlight a few plot points that your group was interested in, and ask the GM how your group can pursue them further. RPGs are a collaborative medium; the players can, and in many cases should, be as involved in creating the story as the GM is. When having this conversation, you may discover that there's a communication problem - perhaps the GM was putting in hints for your group to follow up on, but your group missed them and now your GM believes you weren't interested. Or perhaps you the players aren't expressing your interest clearly enough - the GM may be throwing things at you to see what sticks, but from his POV, nothing's catching your interest. Whether or not there's a communication problem, having a discussion as a group with the GM can help him figure out what your group enjoys.
Again, don't approach this as "Hey, GM, you're not doing plot. You should do more plot." This puts the GM on the defensive, and makes him feel bad and unappreciated. Instead, say things like, "Hey, GM, we're really curious about what's going to happen now that we've killed the politician's daughter. Can we spend some time next session exploring the consequences of that?" This tells the GM you're paying attention to the events of the game and you're invested in the world he's created for you, which usually makes GMs feel excited about the game.
Is the GM just honestly bad at plot-heavy GMing?
Not everyone has the skills to be a prolific novelist or TV writer - likewise, not everyone has the skills to GM a plot-heavy campaign. This isn't a diss on your GM! Figuring out detailed plots, action consequences, character interactions, and other elements of plot-heavy campaigns is hard. Your GM may simply not realize that there's plot to be had in these kinds of interaction, or know how to create it if he does. If that's the case, you again have to decide whether to accept this and keep playing with no expectation of plot, or to leave. But you also have a third option, depending on your relationship with the GM: offer to help him improve his skills.
This one's tricky: no one likes being told they're bad at something, even - or especially - by a good friend. If you really, truly think your GM would like to improve his ability to put together interesting plots based on PCs' interactions with the world, then you can offer to help him. Perhaps go over each session after game time with him, pointing out places where the characters' actions should affect the world and offering ideas for how. Perhaps find a way to do it real-time, where you can say during game, "Now that we've killed the politician's daughter, he'll probably send the police to find out who did it. Or he'll accuse his rival of doing it, thus using it to his advantage. Should we start running from the cops, or should we be on the lookout for his rival trying to find us instead?" Whichever you choose, make sure you're still respecting the GM and his choices. Be careful not to sound patronizing or bossy, and make sure you're not stepping all over his GM authority when offering suggestions.
TL;DR: You need to figure out whether the problem is one of playstyle, communication, or skill, and take appropriate action from there.