According to the Star Wars: Force Awakens Visual Dictionary, after 65 years of continual operation, R2-D2's memory files are indeed horribly bloated.
Apparently he spends much of his time nowadays in a special low-power mode attempting to make sense of the vast amounts of data he's come into contact with, both in terms of his own lifetime and also the data he's hoovered up by downloading entire networks that he's connected to
As R2-D2 recuperates in his self-imposed low power mode, his
diagnostic systems are attempting to organise the vast trove of
information in his databanks from over seven decades of uninterrupted
operation. The defragmenting of millions of exanodes within his memory
is causing R2-D2 to "dream" many of his greatest adventures