The biggest and most common mistake I see among otherwise good players is players not giving *good* reasons behind a pitch. For example, both of these are bad:
From England to France: "Everyone else's press is terrible, so I really want to work with you. Would you support me to Belgium?"
From Germany to France: "Hey, if you support yourself there, you can stop England getting Belgium, and then he'll only have one build and you'll have two."
Both of these are bad. I would probably not ally with either of those players.
Here are some good examples:
From England to France: "Would you support me to Belgium? It's better for me to have it, because if I take it with the fleet then I can't attack you, but we can attack Germany together. Also, if you support me there, then you can use your other unit to swing at Munich"
From Germany to France: "Hey, if you support yourself to Belgium, we can stop England taking it. With Russia going against Turkey, he's unlikely to be able to reinforce Norway for a few turns. So, if we keep England on the back foot, I'll be able to take Norway and Sweden, and you'll be able to take England."
These are good because they give good reasons why I would want to do the thing (beyond "because I like this player" or "because I get centres"). And they show that the player is thinking about the long term.
I will *always* choose the ally who is creating something for themselves to do that is not attack me. Alliances aren't necessarily about taking centres (although it obviously helps)- they're about constructing something that will benefit both of your positions.
This is how you hold alliances together longer term, too - an Austria/Russia alliance's goal isn't "kill Turkey", it's "give the other player something to do that isn't attack me" . To start with, that might be "kill Turkey", but as Turkey is dying, the alliance should be continuing to find other things to do together. It's a mistake to wait until you've squeezed someone out to decide what to do next.
----
Of course, there can be a bunch of rookie press mistakes too, like:
1) not writing enough text:
Russia to England: <Long, detailed message about working together>
England to Russia: "Sounds good."
2) Being overly paranoid:
Germany to France: "There's no way I will ever accept you having a unit in Burgundy, and I want you to only build fleets"
3) Being overly aggressive or grabby:
Austria to Russia: "I'm sorry man, but the only way I am prepared to work with you is if I get Bulgaria"
4) Being overly agreeable:
France to Germany: "Sure man, I'm happy to DMZ Burgundy. I mean, I've already agreed not to go to the channel, and Italy wants to DMZ Piedmont. I'm all peace over here."
5) Not considering that the other player might want something too:
Turkey to Russia: "Hi, let's work together. Why don't I pop your fleet in Rumania with Austria's help, and then you can help me into Budapest."
(What does Russia get out of that?)