[RPG] way for a Bard to learn one more known spell

Yes you get to learn all those spells you mentioned, but magic always comes at a price. In this case while you "know" a bunch of spells you can still only cast a specific number of them each day. So at level 2 you can cast your at-wills 1 encounter, 1 utility and 1 daily spell (not including cantrips and rituals). You just get to choose which one you will, for lack of a better term, "charge up" for the day. Like Peteris said, at each extended rest you must choose which of your spells you will prepare for the following in game day. This keeps you at the same power level as other same level characters (except you get +1 at will that you can use at any time).

So, Bob the level 2 wizard opens his spell book in the morning after getting a good night sleep and turns to his "Utility Spells" page. He sees Expeditious Retreat and Shield, not wanting to get too close to enemies, he chooses to memorize the evasive spell Expeditious Retreat absorbing the spells magic for use later that day. He then flips through his spell book and does the same thing for the daily spells he has in his book. He then sets off on his travels with his companions being able to cast 3 at wills, 1 encounter, 1 utility and 1 daily.

The benefit here is if you know you'll be facing a certain creature and you have a spell that will deal lots of damage to it, you can prepare specifically for that engagement.

This looks to be entirely up to DM discretion.

There are two equally valid positions on this and the rules do not refute either one.

The first is that this is a completely separate spell, and slot, and that the two have no overlap with your casting class. The spell you learned and the slot you obtain are kept separate from the class spells if you have levels in that class.

The second position is that it is a class spell, from your class list and you can retrain it as you would when you take a new level in that class.

The second position is mildly problematic in that you can continue to obtain higher level spells with the retraining, and it may lead to this MC being simply the obtaining of another 1st level spell slot, rather than feeling like a mini MC.

The first position is problematic in that it introducing additional bookkeeping and may be perceived to be overly harsh and pedantic.

In my games, I think I would allow the MC feat to simply be an additional first level spell slot and allow the spell to be retrained if it's from a class that allows that and you take levels in that class. I would probably not make them remember which spell goes with their MC beyond that the extra slot must be a spell from that class. This may be too lenient for some games though.