Relationship advice? Do I keep trying or move on?

It's long; sorry. I've been dating this guy for a 16mo. He's sweet and caring, but certain things annoy the heck out of me. I've been wondering lately if this is a compatibility issue since I've tried talking to him about these things to little avail. Do I keep trying or just move on?

1) He doesn't believe in saving face in public. Ever. In private, I have no problems with inappropriate jokes, but in public, it would be great if he didn't joke constantly about sex, sexual organs, bodily functions, etc. Can't we just have a conversation about something else? But he tells me I'm being "fake" b/c I don't act in public like I do in private. This isn't me saying I like a band in private and then saying I hate it in public. It's just censoring myself so I'm not talking about sex in front of my grandmother or someone's child. I've refused to bring him home to meet my parents b/c I am so afraid he will embarrass me in front of them.

2) He complains about everything, and it's really draining. For example, today we tried a new sandwich shop neither of us had been to before. We order and when he gets his meal, he gets upset that it isn't "unique" enough, saying he could have made this very sandwich at home. I told him to go complain if he wanted, but in my head I was thinking, "the ingredients were listed on the menu. If you thought it sounded boring, why not choose something else?" Of course, they told him they gave him what was on the menu. Instead of just accepting the mistake (we've all ordered something we didn't really want), he starts blaming the restaurant for lying. No. YOU ordered a boring sandwich made as advertised. Doesn't mean the entire place sucks. So I had to spend the whole meal trying to cheer him up. It's like this everywhere we go; he always has to find a fault and get upset. Just enjoy life and stop letting little things upset you. It's a sandwich you had for one meal in your life. Not a big deal.

3) He is pretty jealous. All the time. For no reason. I have never cheated in my past relationships, nor have I cheated while I was dating him. We got into a huge fight over this issue over the summer. I was taking 24 college credit hours (yes, 24) during an 8wk summer session while also helping my sister plan her wedding. Since I wasn't spending as much time with him, he starts listening to his friend who is saying I'm cheating on him. Literally, I saw only him and my family that entire 8 weeks b/c the rest of the time I was studying or sleeping 2-4 hours a night. He finally said he trusted me, but he won't let it die. Now he's always subtly accusing me of cheating. I just turned 22, so the bar scene is new and exciting to me. He's 30, so he's been there, done that (which I can understand). But when I say I want to go to a bar (we've been 3 times since we started dating), he's like, "why, you want to pick up some guy?" Yes, b/c I'm going to take my boyfriend to a bar so I can pick up another guy. I'm getting a little tired always having to defend myself, especially since there's no reason for his suspicions. He always says these comments in a joking way (which he then says he was just kidding after I point out the shoddy logic), but why would you even joke about stuff like that?

Anyway, I've tried talking to him and he just tells me I'm a bad communicator. Things change for a few days, but then it always goes back to what it was before. Do I keep trying or just move on?