I would allow the character, but he would not be a paladin.
I don't have a problem with buying prostitutes, since it's his own prerogative to do so if it's lawful in his society. However, I would just like to mention, as an addendum to the debate on prostitution, that the arguments that support it (as a woman's conscious choice) are equally effective for child labor (in China, for example.) Just keep that in mind.
On the subject of drinking, do keep in mind that alcohol is an
addictive drug that impairs judgment. Drinking in moderation is fine, but you should be held accountable for any actions taken while inebriated. (As an aside, modern day societies don't hold you accountable for purposefully impairing your judgment and committing crimes as a result, but let's not go down that road here...)
I have two problems with Sir Cedric, which make him a fallen paladin in my campaign.
1) He believes he's entitled to rewards for doing what he does. A person who does good deeds to get rewarded isn't good. He's neutral. In D&D (and I subscribe to this notion in real life as well) a good deed is one done with no thought for reward (other than the sense of satisfaction you feel when you do the "right thing."

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2) He is not an inspiration. In my opinion, the code of conduct in the PHB has nothing to do with the paladin himself. It's a tool that enables the paladin to inspire others to the cause of good. The fact of the matter is, as Cedric so bitterly exclaims, his cause is hollow because he is just one man. By inspiring others, Cedric "recruits" common folk to the cause of good, and paves the way for new paladins. This is the most important part of being a paladin--far more important than slaying succubi.
As an aside, I find it rather amusing that so many people in the "what does a 2nd level commoner give a 12th level paladin" thread are replying "herself", but when a paladin pays for it, it's bad...
Hm? If you truly feel that way, you've just equated prostitution with making love to your wife. The difference between getting paid to make love to a person and making love to a person because you
want to is quite staggering in my eyes. Did I misunderstand your point?
In fact, on the subject of being atypical, I think a character like Cedric would work best in a setting where most paladins are the conventional type. The conventional paladin is great, but one of the dangers that it runs (both for the paladin and the people who interact with him) is to shift the focus from the work that he does to the trimmings that go along with it. The shiny armor and the special mount and the flowery speech - these are not what make a paladin. But they are often what people focus on.
There's a middle ground here. On the one hand, you have the paladin who wears shining armor and speaks with "thee" and "thou" on a regular basis. On the other hand you have Sir Cedric who, without switching "sides" manages to directly oppose that concept. In the middle, you have a paladin who doesn't wear polished silver armor and doesn't speak like a noble, but still treats people with fairness and respect and doesn't get drunk and cuss out people because they annoy him. Patience and perseverence are important virtues for a holy champion. If Sir Cedric can be a paladin, paladins will be numerous in your world.
Here's an example of a paladin concept that differs from the PHB that I would allow:
Riemal is the son of a blacksmith, born and raised in Harrathos; a truly unremarkable village in the hinterlands of the Queendom of Kereloc. As a child, he read stories of great paladins (who spoke with flowery speech and wore shining plate mail) but never did he imagine that he would even see the lands outside of his home. To cut a potentially long story short, Riemal's story changed one day when an adventuring party's gambit led a band of devils straight through Harrathos. Sure, the adventurers slew the erinyes that had hunted them for the past few months, but the village was destroyed in the process, and the minor devils made off with numerous survivors. Riemal survived through sheer luck, partially trapped underneath a bunch of debris.
Narrowly evading madness in his grief, Riemal found that the only way he could cope with his loss was to focus on something. He began to search for the lost villagers, determined to prevent their further suffering at the hands of the devils. The problem is just that everywhere Riemal goes, there are other people who have lost loved ones, and he just can't seem to make himself insensitive to their suffering. He just has to help them, too. Sure, he rescued the last missing villager from Harrathos several years ago, but there's plenty of other people who need saving, so he can't rest yet. There's always more people who need help.
At some point, a god took notice of Riemal, and surreptitiously imbued him with the powers of a paladin. Riemal began to notice that he could do things he couldn't do before, but wasn't sure what to think. He's never communed with his god, and he has no idea that he's a paladin. In fact, Riemal is shy, filled with the humility of a small towner, and would never say something as preposterous as "I have been chosen by the gods." Why, even the thought makes him blush with shame. He's just a common man, doing what needs to be done. Sure, he's seen a lot of bad things and there doesn't seem to be an end to the madness outside of the village, but someone's got to help people, right?
Riemal is, above all, humble. He has learned that patience and understanding are the only ways to combat hatred. Within, Riemal is constantly struggling. He fights to keep believing that people are good at heart, but some days--like that day when the queen sentenced the Knights of Everue to death, or the time the fiend Halthyon orchestrated the pogrom of Lion's Marsh--it's a losing battle. So far, he's holding his ground, and he does not let anyone know of this struggle.
Outwardly, no one would guess Riemal is a paladin, but his actions and optimism make him an inspiration to others: He's an attainable ideal, a common man who just happened to land on the road of a hero. Oh, don't tell him he's a hero unless you want a good laugh, though. He's been known to blush and stutter if you do that.
Ouch, that was long. Sorry! It was just so fun to write when I got started.

Note that I didn't say much about the lawful aspect in my example. To tell the truth, I'm not a big fan of lawful good, since lawful is a limitation that embraces a particular society's (or god's) law, which may or may not be "objectively" good. If I were to play Riemal, I would play him as a Holy Liberator from Complete Divine.
Still, the reasons I don't approve of Sir Cedric have nothing to do with the lawful aspect.