This was a pretty good episode. Unfortunately, based on the premise, I was expecting a really great episode, so I only enjoyed it as much as a regular episode. They probably could have done more with it.
Based on empathy with Leonard’s mix of curiosity, nerdishness, and passivity, I totally buy it. He didn’t desperately want the apartment, although it did have an attractive inexpensiveness, but the minor annoyance of dealing with a strange person was balanced by the interestingness of the situation combined with the challenge of passing a test combined with the desire to see something through to the end due to having already invested effort in it.