1. Do you run into problems with characters running out of spell points quickly (a la psions) due to having to scale damage dice?
In my experience this is always an issue with a point system. Points always seem to drain faster than slots. I am not yet sure if it is due to the scaling factor or if it is simply because the greater flexibility tends to a heavier reliance on spells because slots set a caster into a more conservative casting mode than points do. I think it is harder for casters to "pace" themselves with points than with slots, but I personally prefer spell-points to slots for some classes.
2. Sorcerers only get a few extra points beyond what wizards/druids/clerics get. Does this cripple the sorcerer's main advantage over the wizard--staying power?
Personally, I prefer that not ALL classes gain spell points. I tend to grant spell-point pools based on the style of magic involved. For example, a wizard needs to sit down and prepare spells ahead of time. This to me seems to be a perfect match for spell slots. The wizard is basically picking the spells they have prepared that day. Sorcerers on the other hand are simply a magic battery that knows how to form a select few spell effects with their innate power. Perfect candidate for spell points.
On the divine side, Clerics must sit and pray ahead of time for the spells they wish to carry that day. Also perfect for a slot system. Druids however, do not pray for their spells, they draw their power from the forces of nature. Thus, I would grant Druids spell-points.
As for the specific amount of points acquired reflecting the classes...I think that once again, WotC poorly implements the Sorcerer. The Cleric, Druid, Wizard table gives a major boost to these classes, giving them much more flexibility than a sorcerer since their "Spells Known" can change from day to day and gain nearly the same amount of spell points. Yet another reason I do not care for ALL classes converting to spell-points.
3. What does play look like at higher levels? With potentially hundreds of 1st-level spells each day, how do spell point casters divide up their resources?
In my experience, you dont have to worry about hundreds of 1st level spells. Remember that a caster needs to spend 9 Spell Points to cast a fully effective Magic Missle. As for dividing their resources, it completely depends on what the characters are confronted with and the spells available. Overall the point system is more flexible and is not as hard for casters to allocate whent hey will and wont cast a spell. If you want a caster's life to be harder use slots, if easier use points.
Another consideration is that you shouldn't allow certain spells like
Wish to be cast this way as it can quickly unblance the game (not that it doesn't anyway).
4. And lastly, if you have mixed spell points with psionics, how do spellcasters rate against psions when the spellcasters cast from a point pool?
What do you mean by 'rate'? By what criteria?
In my criteria, they each have their own strengths and weaknesses. I dont think I would say one is better than the other.
Hope that helps some.