Parallelism with "should have"

Better not repeat it unless you wish to emphasise an impatient regret there. If you want to repeat it, I would put the sentence in this way:

I should have gone to the mall, I should have bought that dress!

Certainly, it would not be incorrect to do it in the way you are suggesting. Such a context could point to a speaker that resigns to her fate, for example:

I should have gone to the mall and I should have bought that dress.

If, however, your intent is just to state the information without supplementary connotations, then it is certainly sufficient to say:

I should have gone to the mall and bought that dress.

There is no need to repeat the phrase "should have" unless going to the mall and buying the dress were two sperate actions. ie. If buying the dress requires you to go to the mall, and you did neither act, there is no need to repeat unless you need to emphasize you regrets. However, the sentence will be more vague when you add the second "should have."