To the OP:
We always kind of ruled that the dominated person cannot be compelled to cast spells under the influence of a dominate spell because of the complexities of the art.
I don't see anything in RAW that supports this. I would definitely allow the Dominated person to cast a spell if commanded to do so, or if the person had a spell to cast and it allowed them to complete a command given. The Dominator can always simply ask the DP to reveal what spells they have available. I also don't see why you couldn't order the person to memorize spells or pray to their god for new spells. It's a separate question as to whether the deity would provide the higher level spells, assuming the person worshiped a deity.
It's pretty obvious that the dominated person is imprisoned within his own mind and nothing more but a mere puppet.
My take is that this is only true when the dp is given an actual command. Similar to Greenfield's thought process, uncommanded, the person goes about their business and does not realize they are being dominated (for plausibility reasons, you'll have to assume an uncommanded person does not suddenly realize they have been dominated until they actually break the enchantment).
Speaking of Greenfield

...
As far as spell casting is concerned...
Consider giving a Dominated wizard orders to go to the city of Timberlain and kill the head of the Thieve's Guild.
You might not know what spells he has memorized, or what's in his spell book, but he does. He'll prepare his spells according to his own best judgment, and use them accordingly.
I don't think so. Let's look at RAW from SRD and how it is phrased:
Once you have given a dominated creature a command, it continues to attempt to carry out that command to the exclusion of all other activities except those necessary for day-to-day survival (such as sleeping, eating, and so forth).
I don't think spell preparation qualifies as those activities necessary for day-to-day survival and there is no debate it does not fall under the category of "sleeping, eating, and so forth." WotC adding those examples just in case someone tried get away with something. A dominated caster isn't prep'ing new spell, isn't sharpening her sword, isn't even bathing (barbarians don't bathe anyway so no DC there

).
You give someone a command, "Go kill Mailee", they go and do that and keep trying it until the die or succeed with whatever tools they have with them at that moment. That dominated person isn't going home to plot out a strategy or memorize a spell or even pack a lunch.
Now, I would definitely allow the Dominated person to cast a spell if commanded to do so, or if the person had a spell to cast. I also don't see why you couldn't
command the person to memorize spells or pray to their god for new spell. It's a separate question as to whether the deity would provide the higher level spells, assuming the person worshiped a deity.
Yes, a DC 15 Sense Motive check will spot that there's a problem.
Greenfield, as someone who just looks at this from a RAW/RAI, I think you're perspective is tainted by your own campaign and need to uphold/justify the outcome you described in your campaign. Put another way, I think you're looking at the spell with a definite bias on how it works.
Let's look at the text from SRD
Because of this limited range of activity, a Sense Motive check against DC 15 (rather than DC 25) can determine that the subject’s behavior is being influenced by an enchantment effect (see the Sense Motive skill description).
1. First off, there is nothing in the SRD about needing a "problem" to warrant a Sense Motive. Your adding that qualifier should be a red flag for you to reexamine your own interpretation of the spell.
2. The SM DC check has been
lowered by 10. Per RAW, Dominate is one of the few spells that is so obvious you get a DC 15 spell to notice its effects
without there even being a stated problem. DC 15 is arguably trivial for anything that has SM as a class skill and is high enough level to encounter a Vampire. A 1st level Monk in our campaign had +8 on his SM check. Stop and ask yourself what WotC is trying to communicate about this spell--it's bloody obvious when someone is dominated because the control is so overpowering you do nothing else. Contrast that with Geas where the control is more subtle, but the controlled person can avoid some of the instructions.
I tend to think of it as giving someone an obsession, something the simply have to get done.
A real "obsession" is more than something you have to get done. Your annual taxes are something "you have to get done." I would submit you're perception of Dominate is closer to a Geas/Quest spell. Obsession is closer to the behavior of a drug addict or a stalker.
The spell description says that they'll care for themselves normally, in terms of eating and sleeping and such. That says they aren't hollow puppets.
Unfortunately it says the person performs the task to the "exclusion" of everything else. The obsession is so dominating, you get a DC 15 motive check. You don't even have to
know the person. That's something a 1st level anyone could notice.
As for how obsessed they are or appear to be, that's a matter of DM opinion.
I think RAW makes it pretty clear how obsessed they are suppose to be: "to the exclusion of all other activities.." except those needed for
survival.
I tend to make it more or less obvious depending on the nature of the command given.
RAW doesn't allow that. The nature of the command has nothing to do with the SM check. The only leeway you really have is to not give a command. If no command is given, then per RAW no DC check would be warranted. But RAW explicitly states that any command results in "limited activity" and that is what triggers the DC check.
If you establish the control but give no particular orders, I think they're free to behave as they would normally until told to otherwise.
I would agree that RAW supports this.
The Vampire simply ordered him, "Ignore what you just saw and go on about your business."
This is a can of worms I'll avoid
How obsessed can one get with an instant command to ignore something? It's sort of "These aren't the Droid's you're looking for. Move along."
I would definitely argue that the Jedi Mind Trick is not tantamount to Dominate and it's much more along the lines of Suggestion, imo.