My biggest training tool is actually playing slower than I usually do during push and pull phases. I do this so my opponent can more effectively see how I'm zoning, approaching, defending, etc. Once they get used to what I'm doing, I'll simply increase the speed. Their reactions to my play will pick up in response. Once they can contend with what I'm doing vs them, I'll drop the speed back down and switch strats. Rinse and repeat.
One of the issues in the game is that, at the speed most of the high/top level plays, so much can easily go unnoticed if you don't know what to look for.
Punishment, you should obviously try and go all out (at a speed you can be consistent at) until you have a good sense of what combo trees are available to your level of technical ability and then maintain those until you improve. Make that **** your bread and butter. Once you have more speed, you can start getting creative and make the next tier of connections your bread and butter. Rinse and repeat.
Technical errors are much more common if you try to play as fast as possible all of the time. Playing like that is like training for a marathon by sprinting a half mile every day. You want to run at a solid pace for 5 miles and throw in a stretch of sprinting here and there, not blow your load in the first 2 minutes.
In addition, if you go from 0-60 like that and your thought processes can't keep up with the speed yet, even if you don't make a technical error, you will make bad decisions because of a disconnect between current location of character and previous. People that play like that tend to watch their own character more than watching the opponent's. The consequence of doing so is that their reaction to the opponent's actions are greatly delayed.
And you guys all know what happens when you make a technical error or a bad decision: Armada downsmashes you once and death combos you out of it. Mango finds you shielding and goes in hard. Hbox rests you. M2K grabs you. Javi quintuple shines you offstage somehow. Etc.
Basically: Practice doesn't make perfect. Perfect practice makes perfect. Build up to what you want to do, do it consistently for a while, then move on to something else. Go back every once in a while to keep rust off and to ensure your responses are solid.
Edit: I used to get a lot of **** for being a sandbagger because I would do this. I didn't really understand the reasons behind it years ago, but... you know... with age comes wisdom dark side something something.