Later in the series, Peter visits Syler to learn his ability, but Peter comes into contact with Syler on multiple occassions in the first season, but never picked up his ability. Is there something different about how Syler works that prevented Peter from picking it up?
The key to Peter's ability is that he must be empathetic to the person in order to access their ability. Hence the powers name of Empathic Mimicry
Seeing as Peter never had anything in common with Sylar and actually rued his existence, he could never be empathetic with him enough to absorb his ability.
It wasn't until Peter was desperate enough to need Sylar's Intuitive Aptitude to understand a solution to his current situation. He then obtained it from a different version of Sylar from a different timeline, one that had grown softer due to his connection with the child and helped explain to Peter what this ability truly can do.
On Peter's wiki page on the Heroes Wiki, you can see that he comes in contact with all kinds of abilities but never displayed them.
Just to add to Peter's lack of empathetic connection to Sylar earlier in the show, Peter 'absorbs' a lot of his abilities that Sylar has in S1 since he gains precognitive painting from Isaac, flight from Nathan, healing from Claire, time travel from Hiro, telekinesis from (strangely) Sylar and most importantly for that series Radioactivity from Ted. Peter detonates in S1 because the powers he has already absorbed, that Sylar has also has, namely radioactivity are activated by a combination of his anger at Sylar but he does absorb to some extent part of Sylars power whilst he does not copy Sylar's actual power he does somewhat appear to take in some aspect of it leading to him having a lack of control over his power because of his attempt to copy Sylar which leads to him becoming a living bomb.
Later on when Peter travels to the future and meets Sylar in an alternate timeline he gains Sylar's true ability that of intuitive aptitude but whats interesting is the fact that in order to gain this power it does not seem to be as simple as we have seen it previously. Where Peter has usually simply absorbed the power through touching a person particularly early on he does not need to establish much of any bond with the person as when he absorbs telekinesis from Sylar he is able to use it simply by remembering how he felt at the exact moment he acquired the ability something that Claude manages to get him to do. When it comes to Sylar, Peter has to physically fix something that is broken in order to unlock the ability as the wikia explains:
So Peter is able to gain Sylar's ability only when he can fully understand it unfortunately unlike the other powers he has gained it is the most difficult to understand and the most difficult to control hence why we later see Peter back in the present struggling to control his hunger for more powers. It also appears to me that Peter in this episode Peter does seem to partially believe that Sylar's need to kill could be linked to his power as he seems to be cautious of visiting Sylar to gain the power although it does seem more likely he is just afraid Sylar will attempt to kill him Peter does not seem to want to willingly absorb Sylar's ability when first told to do so by future Peter.