Bitcoin core does not have all unconfirmed transactions I am running bitcoinqt and checking for new transaction for payments I made using getrawmempool. Payments were made NOT from/to the mentioned bitcoinqt wallet address.

As I see some my unconfirmed transactions never come to getrawmempool.

Is it expected result or I am doing something wrong?
In general, mempools are not guaranteed to be the same node-to-node. The behavior of the reference client is that once mempools reach 300MB, the lowest fee tx's are thrown away.

It's possible your node has reached this limit (either because it's 300MB or because your default is much lower) or simply because you're connected to nodes that have the same limitation.