Let's face it, in-battle RNG in Pokemon is handled horribly and ruins the core gameplay. An attack randomly missing for no reason just punishes the player for doing absolutely nothing wrong, and likewise, crits can reward players for using the wrong strategies. It's straight-up bad game design.
Here's my take on how things could be remedied:
>Accuracy/Evasion no longer exist. All moves are guaranteed to hit unless the opponent is immune
>Critical hits are gone, along with all the moves that they associated with
>Moves with secondary effects will always trigger secondary effects.
>To go with the above points, many moves are retooled or culled, e.g. Focus Blast has lower power and also lowers the user's Speed.
>Moves with increasing failure chances such as Protect will now always fail on the second turn. Moves that cause flinching cannot cause flinching twice in a row.
>Confused Pokemon now only hurt themselves when trying to use a Status move. They cannot snap out of confusion on their own, and must be switched out to be cured.
>Paralysis and Infatuation now work like Truant, with the afflicted Pokemon being unable to attack every other turn.
>Frozen Pokemon now thaw out after 3 turns. Any Fire type move will thaw them out instantly.
>Capturing is now based on set requirements that differ between Pokemon. E.g. some Pokemon are guaranteed to be caught if their health is in the yellow, others if their health is in the red.
>Sleep/Paralysis increases a Pokemon's capture bracket (a red-health catch becomes a yellow-health catch, etc). Using an appropriate ball (e.g. a Net ball on a Surskit) will also bump a Pokemon up a bracket.

Any further ideas/suggestions/opinions would be great. Feel free to point out flaws I might have missed.