Continuity mistake: In the scene where Tim buys his lunch in a Pret A Manger, the assistant charges him £4.24. When he time travels back, she charges him £6.23. (01:40:05 - 01:41:55)
Continuity mistake: When Mary tries different dresses and shows them to Tim, Tim has increasingly messier hair. At the end, when she tries again the first dress, though, he suddenly looks the same as in the beginning. Presumably the first and last sequences were filmed together, then the rest.
Answer: This is one of the (many) time travel plot holes in the film, and unfortunately your question doesn't really have a definitive, or satisfying, answer. Richard Curtis has said he was less concerned with making an airtight time travel film than with the human story at its core, so he let things like this slide without explanation. However, since we don't see any "second" Tims around when he goes back in time, and no-one else seems to think of him as an "extra" Tim, we can safely assume that, yes, he replaces himself in the timeline when he travels back. (Of course, this doesn't explain what happens when he then returns FROM the past).