Uffdah! This all raises an interesting question: does 'mi lukin pona' mean "I see well" or "I look good (i.e., am handsome or at least healthy looking)?
Surely, "I look at myself" is 'mi lukin e sama' (with all the questions this can raise).
The "try to" sense of 'lukin' (not so plausible now that we have 'alasa') pretty clearly does not apply here, but only on content grounds
How 'sama' works as a verb has not been tested much, I think, but I would expect what the subject seems to be would be the object, not a complement (which are pretty rare), or a verbal -- rather than nominal -- complement.
But then, the lessons do suggest that complements are more common than appears in the corpus, since it seems to solve the "about" problem with complements (and thus adds half a dozen verbs at least)
The 'e ni:' construction corresponds exactly (including connection choice) to the English "that" construction for indirect discourse, so stretching it to other cases is tricky, although using 'ni' to serve as a connection to cover relative clauses is useful, but follows a different pattern.
'kama' takes a VP complement, but not, apparently, a NP one; where you come to in the literal motion sense is introduced by 'tawa'.
'sama' is also a preposition, so one question here is whether it is one here (in which case there would be no 'e'). If it were, it would modify 'ni lukin' as a way of seeing, which doesn't seem to be right, so on the whole, it looks the sentence (with Josan's correction) is pretty much right as it stands -- unless 'sama ...' is itself the object rather than an adverb here. I don't know how to decide that one.