i speak faster than him.
who did you talk to yesterday?
First let's correct your question:
What's wrong with these two sentences ?
I speak faster than him.--> This sentence is OK informally.
If you want to improve the grammar, then you should say:
I speak faster than he does.
Who did you talk to yesterday? --> Most good grammar books consider this to be correct nowadays. However, using the word whom would be more "formally correct."