Analysis of the sentence:
There are three verbs in this sentence: left, washed, and cleans. You'll notice that left and washed are in the past tense. On the other hand, cleans is in the present tense. There is a sudden shift in verb tenses. Consistency of tenses is important in a sentence. Hence, instead of saying "Before he left, Jamie washed the dishes and cleans his room." one should say "Before he left, Jamie washed the dishes and cleaned his room." instead.