About the Replays
Contrary to what some believe, a replay is not saved as a video recording of the match. Instead, the input data from the match and the match's random number seed is saved, so when a replay is watched, the game in fact re-generates the match from the data. This makes replays much smaller in file size than a video file, and it also allows pausing and camera movement during the replay.
If a character or other element is loaded during a match faster than expected (such as because of pausing or online lag), then the replay of that match has to "freeze" and finish loading the element before it can continue.
How to save a Replay
Replays can only be saved if they are 3 minutes or shorter. Replays can also be saved to SD Cards.
It is worth noting that while playing online in the "With Anyone" mode, the characters' scores will not appear on the screen above the characters' icons. However, when battles are saved as replays, the replays will show the score numbers above the characters' icons as if the players were playing a Group Brawl with "Score Display" turned on in the Brawl settings.
Replays and Smash Service
Prior to June 30, 2009, players could send their replays to be used for the Smash Service; after June 30, no more replays, custom stages, or screenshots would be accepted. One month later, on August 1, Replay data was no longer being sent. Replays used for Smash Service are all from Stadium mode, due to their typically shorter length and file size.
Replays on Youtube
On July 31, 2015, a function was added allowing Replays for Super Smash Bros. for Nintendo 3DS and Wii U to be posted onto Youtube. The DLC was free, but a Google account is required to post to Youtube.
The Replay Glitch
Reports from YouTube users state that replays may alter what had been recorded. This is on a multi-user basis, meaning it is not a description or comment rumor linked to one Brawl group. This is fixed in the PAL version.