In the mission where Murray is reunited with the team van, Murray claims that he last saw it floating out to sea on an iceberg in Canada, to which Penelope replies that given ocean currents, it would be "highly probable" for the van to drift there. This is in fact false, as the Kunlun Mountains, where the level takes place, are in fact landlocked. While two rivers (the Yangtze and Yellow rivers) originate in said mountain range and empty into the Pacific Ocean, the van would still be unable to float to the Kunlun Mountains because rivers flow downhill, and since the van was not being operated, it would have no way to flow upstream.
In "Operation: Wedding Crashers", Sly is told by the Panda King, that if any of the vases break, it raises an alarm. However, when you go to the temple earlier, and break the vases, nothing happens.
Sly's full motives for venturing into the Cooper Vault are never stated.