Well there's always two fronts to a coach's observations. Your opponent's weaknesses and yours.
Not sure if you're talking about singles or doubles so I'll try and keep it general. Also at your level of play, you're probably looking at very small differences.
The areas I would focus on observing in your opponents are:
1. Their choice of shots. Where do they tend to play the shuttle when under a specific situation? This helps massively in singles when you're trying to rule out corners. Usually people will stick to safe shots when under pressure or being rushed. So if you are able to rush them and anticipate a likely next shot then you've got the upper hand.
2. Defense. Difference in their strength of smash return when placed at different areas around them. I.e. target different positions on the body, difference in forehand/backhand returns. For example, do they tend to return smashes on the forehand side of their body with a backhand? What about varying the speed?
3. Position. Where do they stand, how do they stand - when under different situations? Very important in doubles.
4. Reading their technique. For example, some players tend to supinate a bit less when they are going to play a drop.
5. Character. Knowing the personality of the player. Some players are affected by certain things that upsets their concentration while others play very relaxed and hardly ever get affected by external factors. Back in the day when Gade was at his prime, LD used to wind him up during matches, delaying receiving, talking to the umpire, early shuttle changes, anything to distrupt PG's concentration. And PG really suffered. I definitely don't advocate this but put it in for completeness.
There's a whole load of other things one can observe, down to things like the type of grip they use, how much weight they put on each foot under different circumstances, do they lean more to one side in defense, what players do they do worst against? What tactics do they adopt most?
Level - Semi Pro (though this is a very subjective term)
Is there any specific format to note down the things you have mentioned - footwork, stamina, smashes, backhand, defenses, tendencies, etc?
I'd say just note where his strength and weaknesses are compared to yours and slightly alter your game strategy from there. For example, if he has a very hard smash with excellent placement, then maybe you give him more net shots than clears. If you notice his stamina is worse than yours, then you might want to play longer rallies. If his backhand is weak, then try to make him use it often. If he tend to return a certain shot to a certain place, take note of it and beat the shuttlecock there. If he's a great defensive player, you might not want to smash very often even if that is your strength.