My character was affected by the dominate person spell (and failed the will save) and was given some orders. Does he have any recollection or memory of the orders after the duration of the effect expired?
A creature that's been the victim of a dominate spell usually remembers the events that occurred unless steps are taken to make the creature forget
In Pathfinder, if the creature couldn't otherwise choose to forget, the dominated creature can't be ordered to forget.1
The spell dominate person et al. says that
You can control the actions of any humanoid creature through a telepathic link that you establish with the subject's mind.
Emphasis mine. Among typical creatures, there's no action for forgetting. So while a dominator can totally command the dominated creature to forget something, doing so won't have any more effect than commanding the creature to experience love for the dominator, suffer pain, catch a disease, remember its own birth, see something ethereal, or poop out a squirrel. Having the dominated creature perform such (presumably) impossible actions are beyond the scope of dominate spells. (If the creature does have special abilities that enable it take one or more of these actions, however, all bets are off and the dominator can command away.)
So the creature, in fact, remembers the entire dominated experience, and, actually, the creature can't just forget it. Further, as memory is so closely intertwined with the fundamentals of personality, dominators may know that even commanding a creature to perform such an act is "against its nature [and the creature] receives a new saving throw with a +2 bonus," but that's probably a bit extreme.
A very careful dominator could make it difficult for the creature to understand the actions the creature undertook while under the influence of a domainate spell, such as commanding the creature to close its eyes or cover its ears, but those are actions which can be performed.
So while under the influence of the dominate spell, the creature's memory remains as functional as his mental abilities, experiences (personal and perhaps game-mechanical), and abilities allow. Properly speaking, recall isn't governed by any particular ability score (although Intelligence appears the most likely candidate, arguments can be made for Wisdom and even Charisma—My sense of self is so vast that anything I experience matters deeply to me or whatever), so determining the extent of typical memory is up to the GM. However, unless steps are taken to make the dominated creature's memory of its dominated experience fuzzy (e.g. the enchanter commands, "I order you to consume booze until your memories of my commanding you are a blur," and then lets the spell run out), a creature should be able to recount anything it's done as the enchanter's puppet, and such memories should be as accurate as anything else its done in its life, limited only by the GM's judgment of the creature's ability scores, special abilities, and experiences.
This, by the way, may help explain why vampires are frequently depicted as throwing the best parties.
1 Dragonmarked for Pathfinder's antecedent Dungeons and Dragons 3.5 on Mnemonic Training says
Just as Autohypnosis can be used to memorize text or phrases, it can be used to forget them. Each successful DC 15 Autohypnosis check allows a character to expunge a message he has read or heard (up to 800 words) from his memory. Multiple checks allow a character to forget longer conversations or documents. [...] If you do not use the Expanded Psionics Handbook in your game, characters can accomplish this task using the Concentration skill but with +2 to all DCs. (75)
Whether such techniques can be used by anyone or only those of House Sivis in the Eberron campaign setting is the GM's call, as is whether such techniques can be used to forget events as well as conversations, phrases, messages, and text. The skill Autohypnosis is available from 3rd-party publishers in Pathfinder.
By RAW the target remembers, unless something else happens to make the target forget. But I would argue that the caster can safely order the subject to submit to modify memory spells or similar effects, as this isn't obviously self-destructive.
RAW, nothing about Dominate Person says that the subject forgets about their dominated activities by default.
Mind-affecting spells are often a place where effects are subtle and ill-defined however, if the dominator explicitly orders the victim to forget everything they've done, I'd probably allow it to persist past the duration. If for no other reason than you want a vampire's dominated victims to be pleasingly unclear on what happened...