Way back on my blue version, I trained my magikarp by using all the PP from splash, then using struggle to do all my damage for me, using a plethora of potions in the process. Did this from level 5 all the way up to level 15 for that Karp...
My friend who first got Red, and introduced us to it, brought the game round to my house one day. Three of us took turns playing it, just attacking and fainting rattattas and pidgeys with his Charmander, because we could not figured out how to get past the cranky old man with the catching tutorial (we had forgotten about being given Oaks parcel). We carried this on for roughly three hours.
I thought that poke'dex numbers were all stages of the same poke'mon, so you would get a Bulbasaur, who evolved into Ivysaur, then Venusaur, then Squirtle etc etc...
Due to the specific timings of my battles, I spent an embarrassingly long time believing that your starter evolved once when you beat Brock, then again when you beat Lt. Surge. Was not until I got poke'mon Silver version that I realised this was wrong (Due to playing Yellow, and Pikachu not evolving at all I didn;t realise my mistake on my second game).
As you can likely tell from the above, I did only train my starter for a long time.
I also was guilty of many of the classic mistakes. Psychic being super effective against grass, B+Down to catch, Poke'mon only being taught moves that fit heir typing, etc.