1. Languages by race. Why does my Tiefling who grew up in a human city automatically know Infernal? I would say Background has more bearing than who your parents are. My in-laws are french, but they raised their daughter (my wife, duh) to speaking english in the home. English is her first language and she doesn't really consider herself bilingual.
2. More language nonsense - bring back max # of languages knowable as a function of your Int score. 5e is all about stripped down and easy to learn so your Int modifier seems to make the most sense.
3. Weapon Proficiencies. Again I like the stripped down, easy to learn aspect of 5E, but I think there really could be a third tier here. In fact I would go so far as to say weapon damage could be based on the character's proficiency. Simple weapons do 1d4, Militia weapons do 1d6, and Martial weapons do 1d8. Go up on die size for two handed (including versatile), go up one die size for heavy.
4. Finesse & Ranged Weapons. Adding Dex to damage is a big nope to me. Dex mod for to hit rolls - sure, but not to damage, except in rare cases.