For one thing, the manga actually has a totally different introduction: the pilot issue before the first arc. That introduces Tsuzuki in a considerably more serious and responsible light than the anime does. It doesn't play up his sweets-craving nearly as much, and it's made clear that it isn't just that no one wants to partner with a slacker like Tsuzuki--he's also the training wheels and counselor of the division, and all the new or unsteady transfers get sent to him.
It's also made clear that Tsuzuki, not Hisoka, is the one who's most willing to bend rules, to break into locked archives, to save people who should be dying, even if this involves lying through his teeth. And the division chief knows this good and well and condones it. Hisoka himself is presented in a businesslike and competent light from the start. The manga also did without the silly maneuvering the anime had to go through to make him drink one glass of alcohol by accident; the original drinking contest makes his resultant passing out and hangover far more reasonable.
The things that most caught my attention, though, were the differences in Muraki, and Hisoka in relation to him. The anime implies very strongly, right from the start, that a) Muraki wants to seduce Tsuzuki and b) Muraki raped Hisoka. The manga, by contrast, does not have any seduce-Tsuzuki moments in the first arc and states particularly that Muraki chose to use a wasting curse on Hisoka instead of "merely" killing him right then and raping him to make it look like a garden variety sex crime.
I actually have to wonder whether Muraki was intended to be a one-time-appearance villain. His madness is certainly presented in a straightforward fashion, far more simply than the eventual concatenation of his obsessions becomes; he is simply a doctor who despairs in the face of death and cracks. The mechanism by which he becomes able to absorb the spiritual energy and abilities of those he kills is never addressed, and there are no suggestions of the past he eventually acquires or that Hisoka has any particular fixation on his killer. Indeed, the manga presents Hisoka as already knowing he was murdered and fairly calm about knowing the one who did it.
All of which simply reinforces what I've always thought about the anime, which is that it's pretty and colorful, and the voices are nice, but it really isn't a patch on the manga.