I found this question in MGMAT:

Ritika was late to pick up her cat fron the vet after abandoning her broken down car on the side of the road, a 1989 Peugeot.

I agree that this is a misplaced modifier problem.

But wanted to know that whether it has "Verb Tense" problem also. As per me the sentence should have Past Perfect Tense i.e, ".......after had abandoned her broken down......"

Please help me.