In my experiences with what I take to be time travel, memory was affected in the following ways:
*Most noticeably, I could remember the future as well as the past.
*However, the future I remembered did not necessarily belong to the same world I was living in then (after time-traveling). This lent a certain quality of unpredictability to my memories. For example, I couldn't necessarily remember the 'real past' of the world I was living in afterwards, as it was possible that the body that I time-traveled to really lived a different life than my own past to which I originally wished to return.
*In general, because of this, memories become less trustworthy. But, usually, it is just a mistake of confusing the future with the past, or one person with another.
*In general, there are more memories, and more types of memories, but not exponentially more, because it is just an additional factor of future as well as past memories. Arguably, however, this could make it twice as complicated.
*However, understanding time as a continuum with past and future makes memories more coherent, since they are not always arguably gone forever. The same events might happen again, so memories are more relevant than before.
*In fact, once I found that I even re-created the same work of art again, meaning that there is a high amount of inspiration which is just built into experiencing a certain time.
*So, there is more awareness of what memory means, but less trustworthiness about the real past and the real future.