Well, the main issues are this:
1. Caster levels not stacking making spell caster spells weaker and weaker as the character levels.
2. Dipping into a class for 1 or 2 levels to create broken combos.
3. Different results coming from the order you take two different classes in. For example, going rogue 1/fighter1 verses fighter 1/rogue 1 is not the same character.
4. Saving throws being min/maxed by clever multiclassing so all of your base saves by level 20 are +12/12/12 or greater. Even using multiclassing to get +14 on some.
5. Overcomplicating characters with dabbling in lots of classes or taking 1 level in every class.
6. Class features not progressing properily to be useful at high level (i.e. turning undead)
These are some of the major issues with the current rules.
1. If you're worried about losing caster levels then don't multiclass in the first place. It's that simple. Warriors lose a lot of BAB and HP potential for going into a wizard/sorceror class, so it's a decent trade off.
2. What broken combos are you referring to? I'm just curious. Also, if it's a known broken combo, just DM it up and say "No".
3. Of course you're going to get very different characters if you take the level of rogue or fighter at 1st level. The rogue-->fighter is going to have a ton of skills and skill points while the fighter-->rogue will have more HP (though that's about the only advantage I can think of). It's all a matter of what flavor you're trying to add to the character.
4. Just use the fractional bonuses for Saves and such. I know it's a hassle, but if your players seem intent on abusing multiclassing to get huge bonuses.......
5. If a character takes one level in every class they'll be very complicated, but they'll take a huge XP penalty if they then don't keep all those classes within a level of each other.
6. Well, part of multiclassing is giving up some of the perks of one class to gain perks from another, so I'd just say let them deal with it. If they don't like losing out on spellcaster levels, turning ability, etc. then they shouldn't multiclass in the first place.