He had sensible limitations in S1 but those went away and it got bad in S2. Just one example, Adam kills that woman (one of the original metahumans) in an exceedingly suspicious way and Peter doesn't give Adam a quick scan to see what's up. I could accept that Peter is excessively naive which is why he doesn't scan minds as a matter of course, but at that point, he'd have to be brain-dead not to do it.
It is still true that Peter's power was limited. He learned to overcome that limitation and it was fine. I've said this a million times, but if you can't write an interesting story about a guy with Peter's powers then you lack the imagination to work in any kind of professional fiction.
Oh, and Victoria Pratt didn't have a power, just so you know. She was the Company's original Mohinder.
His time travel ability also raises the issue of why he can't travel back in time and solve pretty much any problem that arises, or at least try. They had an interesting angle going with the plotline where Peter swipes Sylar's power in order to know how to change things - time travel alone doesn't tell you what to do, and you just might make things worse - but that was just one of many plotlines that went nowhere and were unceremoniously dropped.
That was a shame, sure. Hiro's power has two limitations. First, Future Hiro indicated that traveling back in time to warn Peter to "save the Cheerleader" ran the risk of causing a "rift".
Second, his experiences with trying to save Charlie and then with Adam Monroe prove that time travel invariably doesn't solve your problems and often causes them in the first place.