There is no dispute amongst the followers of the Ahlul-bait (peace be upon them) that the Prophets and the Imams are sinless, in such a way that they do not commit what opposes the religion. Our scholars have explained in their books of beliefs the evidences to prove this concept. There is no doubt that the Prophet and the Imam are appointed by Almighty Allah. He has ordered people to follow them. So, if it is possible for them to commit sins, they might order people to do so as well and people have to follow them. So their orders would not be trusted to be from Almighty Allah, and He will not order us to follow somebody who can misguide us. Similarly, they are to be taken by their followers as role models. If they were to commit sins, others will be encouraged to do the same.
There are lots of zyarats reported by the Ahlulbait (Peace be upon them) like the Jamiaa, Warith and Ashura also there are lots of supplications like Kumail and the supplications of Sahifatul sajjadia.