Watching matches in slomo is a GREAT habit to get into, and one that's helped me a ton since I've started doing it. I usually follow this process for the quality matches that I study hard:
1. Watch the match at full speed for entertainment purposes. This helps to get rid of my tendency to combo fiend. I have a feeling when a lot of players try to "study" a match, they are almost entirely focused on the punish game and how sick-nasty it looks. Plus, as much as I love competing in Melee, a big part of competing in something is to also be a fan of it. I enjoy watching all different sorts of matchups even if I know only 1% of what I see will ever affect me in tournament. It does help to know a lot of the mid tier gameplans overall, though. I wouldn't bother going through them in slomo because the details aren't critical, but getting a general idea of what characters are going for absolutely helps you be ready for those uncommon matchups in tourney.
2. Rewatch the match at full speed looking for overarching patterns. Don't obsess on the details too much that you end up replaying the same bit of video over and over. You just want to get a good big picture of the match, and often set in general. What were the players' tendencies? What was the recurring theme of the match? As an example, try to figure out what the recurring theme of this game was, but make sure you MUTE YOUR COMPUTER FIRST. Then, replay it back and listen to the commentator's opinion of what the major theme/goal of the match was for both players. If you didn't say the same thing he did, what did you say instead? What does your answer vs. the commentator's say about you as a player? (Please spoiler your comments pertaining to the video if anyone decides to do this, though most of you may recognize it).
3. Watch the match in slow motion. Keeping the major keys to success you noticed above in mind, look at the details of how and why it is working. Rewatching sections as many times as possible is great as long as you are actually gaining from it. Don't expect to just rewatch a segment 50 times and suddenly understand it. You have to constantly alter your perspective of what happened and challenge your fundamental beliefs. Someone may watch a successful techchase over and over and just keep attributing the success to guessing correctly. If the whole match is filled with what look like correct guesses despite the opponent mixing up his DI and tech direction, you will feel like it was luck or some abstract skill you cannot obtain. If you challenge the idea that it was even a prediction at all, you may realize, "OMG, he's spacing himself to bait certain tech options and still punishing the most difficult one." "OMG, he's only going for regrabs until he feels the opponent is trapped sufficiently, which effectively reduces his tech options to 2 spots instead of 3." You won't notice these things if you refuse to see stuff at anything past face value.
Neutral is probably the hardest thing for me to study, but I feel like I've gained a lot by constantly keeping in mind both players positions on the screen relative to each other, the direction they are facing, and other states their characters are in (landing lag, hitstun, dash animation, etc). Being above an enemy is generally considered a bad place to be, but if the player only positioned himself above the opponent because the enemy was dashing away and he knew it would be safe, then that's something important to note. If you go through in slomo and even pause constantly, you can evaluate and reevaluate a situation frame by frame and figure out what went right or wrong for each player.
4. Watch the video once again in full speed. I think your fear of getting used to evaluating situations slowly is a legitimate one. To sort of counteract this effect, once I've sufficiently broken down a match mentally about what was going on, I rewatch it and try to notice everything I did before at full speed. If you noticed a really subtle spacing of a move or WD or DD in slomo, you have to be able to notice that same subtlety at full speed. If you pass that segment with the subtle spacing in the back of your mind, you need to rewatch the entire match and force yourself to bring that spacing into your consciousness.
The more relevant an aspect of the game is, the more focused you should be on it. If the spacing of a particular laser was largely inconsequential, I'm not going to obsess over it because Melee is very much about rationing your focus. You can't focus on everything, so knowing what to focus can often be more important than figuring out what to do. A lot of situations have an obvious answer, but if you miss the question, you're kind of ****ed, aren't you? I will sometimes repeat steps 3 and 4 a couple times to really forge those concepts in my memory.
5. Watch other videos of the same players (easy way is to use the next game of the set) that you haven't seen at all yet. Watching at full speed, look for the same concepts you identified earlier. When you go through this process again with the next game, in addition to the other stuff you are trying to notice, try to keep track of what you missed on your first study of the second video. You may notice you aren't lending enough attention to spacing or grabbing or aerials or defensive movements or your opponent's tech patterns. If you realize you aren't instinctively picking up on these concepts in the second video, then for the third one take extra care to really focus on them the first time you watch through. Eventually, you'll be noticing concepts without even trying.
Spacing around shield grabs was one of the first really distinct concepts I learned from watching Mango vids, and these days I literally think about it every time I see a player hit another player's shield. More importantly, when I am playing, that same analysis carries over and I am able to subconsciously space around shield grabs without having to devote huge amounts of focus on it.
I like to think of watching Melee matches as listening to a new song. First, you just enjoy the experience. Second, you try to figure out what the song is about. Analyze the overall format of how the song is composed, and think about what impacts that may have on the song as a whole (how a chorus is repeated or how verses are constructed can really be the factor that makes a song stick out to you in both a good and a bad way). Third, you want to look at the mechanics and details of the song that make it so effective as a means of storytelling. How does the artist emphasize different words/beats/notes to achieve a specific feeling/meaning? What does their word choice and instrumentation say about the emotions of the song? How would you have tried to create the song if you only had a vaguely similar concept? What does your imaginary take on the song say about you as an artist or fan of music?
