My understanding is that Catholics believe that the pontiff is also infallible, similarly the patriarch of the Orthodox Church is held to have infallible views in regards to religion.
Shia muslims believe their Imam's are also infallible.
First let me clarify that proclamation of faith or Shahada does not say Muhammad, pbuh, was infallible it merely states (in entirety):
"I bear witness that there is no god but Allah and Muhammad is His Messenger"
Muslims hold the belief that the Prophet Muhammad, peace and blessings of God be on him, was the perfect human being. He encapsulated how a human should behave in a vast range of circumstances - as a son, nephew, grandson, as an orphan, shepherd, trader, employee, husband; as an oppressed person, as a person in charge of oppressed people, as a father, as a revolutionary, as an emperor (head of an empire) and above all, as a Prophet.
In all his dealings with others he exemplified piety, generosity, humour, forgiveness, justice and sagacity.
You ask for evidence of his infallibility - I refer you to the numerous books written about him. If you want a book by a non-Muslim, I can recommend Karen Armstrong's biography of him - she is a Christian and a former nun and has written a number of books on religion, just check out Amazon.
However, note that infallibility in matters of religion stems from the fact that all the religious teachings were revealed to him by God, and as such
these are infallible. (i.e. definition 3 above)
In day to day life, there are instances where the Prophet did make mistakes in interpretations - there are at least two such instances recorded in history:
1. once the prophet was asked about how to treat some seedlings and he gave some advice, which was followed. The seedlings died and the agriculturalists amongst them advised that they should have been treated differently (I forget the details, but I think it was about where they should be planted). The Prophet was recorded as saying that he was a prophet and not an expert on agriculture and in this instance other advice should have also been presented to him so that he could have made an informed decision - in this case his opinion was based on his opinion and not revelation from God.
2. Ahead of the treaty of Hudaibiyya, the Prophet (pbuh) informed his companions that they would be performing the rites of pilgrimage that year. When the treaty was signed, the conditions of the treaty were that they muslims would not be allowed to perform the Haj that year, but would be allowed the following year. History records that on this occasion the companions came very close to questioning the instructions of the Prophet (when he instructed them to return without doing the pilgrimage). History records that he told them that God that year had accepted their pilgrimage without them actually physically performing it that year. Thus, scholars say that Prophet's revelation was fulfilled in spirit if not in practice.
(Note that some - if not many - muslims do believe that the Prophet was completely infallible, despite the examples above - scholars merely make the distinction between infallibility in terms of revelation and his words clarifying anything to do with religion. In that regard, he was infallible and the body of work of Islamic literature is testimony to this infallibility.
Cheers,
Shafique