The first is that how we think is deeply intertwined with language. There's tons of evidence of this, not the least of which is Helen Keller's description of her world before she learned language. We'll probably never know what language existed 50,000+ years ago, how sophisticated or simple it was and how it affected how our ancestors thought.
The second is the evidence we have from the ancient world, which was a mere 2,000 years ago. We have written records going back another 3,000-4,000 years before that. I find this period fascinating for many reasons but a big one is how alien we would find the ethics and how societies worked. So would we even be able to relate to Homo Sapiens (or Neanderthals for that matter).
Some things we'd be able to related to (eg the earliest burial rites we've found evidence were from ~75,000 years ago) but I imagine a lot we simply couldn't.
Some Neanderthal DNA exists in the modern gene pool. That itself raises many questions. Was this violent? How was it viewed? Were these people viewed the same? How dominant were large family/tribal groups?