A home seller has an obligation to disclose neighborhood noise problems or other nuisances to a prospective buyer. The seller's tenants, on the other hand, have no obligation or duty to you, as a buyer. If the seller was aware of problems with a neighbor, he/she should have disclosed that fact to you within the time specified in your purchase agreement (in the Real Estate Transfer Disclosure Statement). If the seller failed to make the disclosure and you only found out about the problem after escrow had closed, you may have recourse through the courts. Is it possible that the seller was unaware of the problem? I suggest you contact a real estate attorney.
Sometimes "neighborhood problems" are difficult to define. What might be a problem to you might not be to someone else. Let's say that a neighbor practices her guitar playing several afternoons a week. This might not pose a problem for an owner who is away at work or who enjoys listening to the music. If you are a day sleeper or just hate guitar, this could be a big problem for you. In any event, the first course of action should be to try to resolve the problem with the neighbors involved.
I'm a little confused by your question. You mentioned "old tenants" and "neighbors upstairs" but said you were purchasing a house. Can you clarify?