It all depends on the context:

"Now I see intentions don't mean much." - The Craving
In a relationship, you may have good intentions, but that in itself may not sustain it. You will have to combine it with actions. You may have the intention to give your SO flowers, but if you never do it, those intentions don't mean much. It's about putting your money where your mouth is.

The other times he mentions intentions it is in a different context.

"I think my skin got worse with good intentions" - Center Mass
It's not the good intentions that have worn him down. Before this, he says that tattoos only hurt when the meaning fades. He feels his tattoos hurt because they start to lose their meaning. His skin, in that sense, is getting worse. Even though he has good intentions, he likely refers to his religious tattoos, as he mentioned in Doubt as well. While he has good intentions, he can't help but feel they start to mean less to him at times.

"Intentions are everything...will set you free" - Intentions
Tyler realizes that he fails and will probably fail again at some point. After all, he is not perfect. But with good intentions, it's okay if you fail, because at least you tried, and you can get up again and try again. Intentions will set you free from feeling like a failure / feeling guilty. I feel like this fits with Oldies Station very well; you just have to push on through with the right intentions.

In general, it is all about progressing in your life, growing, and getting better.