First, a couple changes to the way skills are aquired:
1. I would allow skill points to be spent anytime, not just at level up
2. The "one point per level rule" would be abolished: Instead, your level would affect the maximum you could raise a skill. In other words, a new skill could only be raised one per level, but an old skill could be raised more than one point.

General changes:
Learning: Eliminate. I don't like the style of gameplay this skill promotes.
Meditation: Bonus becomes non-linear, in order to accomedate the high costs of skills. I am thinking skill level squared.

Class specific changes:

Explorer:
Knowledge of Herbs: Now only a 5 level skill, allowing the random element to be removed. Further, if you gather herbs and then raise the skill, it would be possible to go back and gather the herbs you missed. (Again, the current version of this skill promotes a gameplay style I don't like.) Skill might cost something like 6 or 7 skill points per level.
Knowledge of Terrain: Now only a 5 level skill (cost maybe 2 or 3). Base time taken to travel over terrain is rebalanced against this now weaker skill (still 20% per level). As a result, this skill is no longer absolutely mandatory for crossing the desert.

Arcane Soldier:
Flame/Icy Strike: Cost 1 skill point per level. PP cost increases by only 1 per level. Extra damage/effect no longer dependant on weapon: now only depends on skill level. (The current version encourages keeping the skill at level 1; this changes it.)
Lower level spells have their costs lowered to match the Mage's costs.

Paladin:
Aura of Healing/Protection: Cost 1 skill point per level. Not sure if the PP cost should be changed.
Again, lower level spells have their cost reduced to match the Cleric.

Thief:
Now learns Envenomed Strike. (Cost 2 per level, learned at level 10)

Bard:
Now learns Shurikens (cost 2 per level). (Enemy Bards use them, so why can't yours?)
Effects of many songs increased. Some songs made more reliable.
Songs now affect the whole party, not just nearby allies.
New skill: Song of Healing. Works similar to Regeneration, but affects the entire party. (Maybe learned sometime in the teens?)

Cleric:
New Spell: Group Heal. Acts like Lesser Heal on the entire party. Learned around when Greater Heal is learned, or perhaps sooner.
Divine Restoration: Now affects the whole party. (Really, 200 PP for a spell that only heals *one* character is a bit much. Then again, this might cause balance issues with the new Meditation, so some tweaking might be necessary.)

Mage:
With the Meditation tweak, further changes might not be necessary.
Maybe a skill similar to Divine Prayer?

Divine Summoner:
Summons cost only 1 skill point per level, not 2.

Thye did exactly like this in Might and Magic VI-IX. Learning was ok skill in MM VI because of respawns, was good, but not mandatory.
Each skill had 3 levels of mastery (in MMVII-IX: 4), so Meditation Expert gives more SP per skill point than normal Meditation. Even more so, iirc promotions also increased benefits from Meditation/Body Building.

On other points: hybrids are meant to be hybrids, hence high cost of skills for them. On other side, class-defining skills are too expensive.. I liked the general way of it in Might and Magic VI-IX. Skills cost the same for everyone, their cost increases according to skill level and you get more skill points per level up at 10 level intervals, making it easier to catch up on some skills. Might and Magic VII+ was a bit more restricting than VI, it didn't allow hybrids to learn higher ranks of skills (Expert, Master, grandmaster).

The way I see it, hybrids are meant to be more diverse characters than pure fighters/casters, and increased costs get in the way of that.

A better approach is to only delay the aquisition of more powerful abilities. So in particular:

Perhaps the cap on weapon levels might rise at a rate slower than one per level, at least past the early levels. (Testing would need to be done to make sure such characters are viable physical attackers.) As is, hybrids are no worse at physical attacks (except for the later appearance of Strike skills) until Weapon Mastery shows up.

For spells, they are already learned later; they don't also need to have a higher cost in addition to that. Even without the higher cost, a Paladin isn't going to be healing as well as a Cleric.

Edit: There are a few other balance considerations. For instance, Arcane Soldiers ought to be better offensive casters than Clerics. (This turns out not to be true against single targets for many levels.)

Having just read about the new 2.0 version with mod support, it looks like some of the changes I would make to skills might actually be possible. Specifically, many of the cost and requirement changes might actually be possible to make. The changes to skill point use caps might not be possible, but many of my other proposed changes (like making Knowledge of Herbs a 5 level skill) might be doable.

Are there any likely balance issues with these changes that I am not aware of?

The whole game will be rebalanced. If I were you, I'd make backup of the unpatched game, just in case, as they change things like resistance caps (no more immunities) and such.

Changes to skills are possible to do even now. Personally I will look toward editor for the things like allowing respawns (no-respawn is the root of all problems in game, skill points' starvation is merely result of this). You can do it without editor now too, but you need to go through each and every area manually and you basically change amount of encounters from 5-6 to billions. Which isn't exactly an elegant solution.