You're correct-- it is grammatical but not idiomatic in this context. You would more likely say "your job is easier than mine". Although maybe don't actually say that to someone unless you want to get punched. ;)
Both are acceptable, but they mean slightly different things. In this context, the difference hardly matters.
My mobile is getting slow.
Slow is being used as a simple adjective to describe the mobile phone. The phone is in the process of becoming (getting) slow.
My mobile is getting slower.
Slower is a comparative form of 'slow'. Slow, slower, ...
It does not make sense that the first definition of mean would have gradations. "the meanest annual rainfall". No.
However, the other definitions are standard adjectives. Therefore, one can imagine saying "meaner" and "meanest" for them.