Ah. This is one of those things that only comes with practice. Note the verb before Dire, potuto? That's the past participle of potere, which is a modal verb. Modal verbs are "auxiliary verbs"; they don't stand alone but in Italian are followed by the infinitive of another verb, in this case "dire", to tell. The same would be true of most if not all other conjugations of potere; posso dire, I can tell (or say, etc), può dire, he can can tell, or, in this case... avresti potuto dire, could have told. (The three verbs form a whole in this context.)
Basically if you see a conjugation of dovere, potere or volere, you know that it is followed by an infinitive. (Why? Because that's just the way the language works; unfortunately I can't give you a better answer than that.)
A good question, though; I doubt you're the only one to have had it.
"Potuto" is the past participle of potere. ( http://www.verbi-italiani.info/en/conjugation/111-potere.html )
No, the expression does make sense, but it's not one that you'll encounter in everyday life unless perhaps you're a crime novelist. You can just imagine a poor damsel who ended up over her head in some dastardly crime saying to Hercule Poirot in the final chapter, "But what else could I have done?", and Monsieur Poirot replying "You could have told me everything, Mademoiselle". Duo has a liking for crime.
"you could have told me anything," and "you could have told me everything" don't quite mean the same thing. The first one means you could have told me whatever you chose to tell me among an infinite set of things, and the second one means you could have told me all the things about a particular issue. Mi avresti potuto dire qualcosa would be "You could have told me anything."