Hello people, I'm new to the forums. I wish to make a few simple suggestions regarding the replays:
1) Give the player an option to auto-save replays, up to a certain limit (for example, once reached 20 replays start overwriting the oldest ones). It'd be useful to review combats without the hurry and decide whether to save them permanently or not.
2) Enable pausing and slow motion in replays. I can see no reason why this is not already in the game! Without this features you can barely see the details.
3) Fix the A.I Uke fights that sometimes don't let you see or save the replay, but instead instantly throw you to a random server as soon as he is DC.
Thanks for reading.

To pause during a replay press 'p'. to skip one frame at a time press shift+p.

There already is an autosave system.
When in-game, go to Setup -> Options, and put a tick on "Autosave replays". The replays will be saved in the autosave folder of your Toribash folder.

Other than that, pausing is indeed already there, though slowmotion isn't.
The third one is a problem even if you are doing a single player replay or playing in multiplayer. Should be fixed soon.