...then walk away right now. The two protagonists and their courtship is shoujo through and through, but pretty much everything else about this manga will appeal more to a horror-mystery fan than to the average shoujo romance fan, which is hardly surprising considering who the original author is.
I'll address a few complaints I've noticed people bring up time and again:
(1) "Too much information/text. I didn't come here to learn so much about Japanese supernatural and horror archetypes!"
This is a typical response from someone who expects the same thing from Ghost Hunt that they do from every other "exorcism" and "spirit-banishing" story: some random horrific occurrences take place, a medium or psychic turns up and guesses the origins of the creepy phenomena in one go, there's a quick exorcism, the spirit is dispelled, and the MC's spend the majority of the story flirting instead of conducting paranormal investigations like they're supposed to. Ghost Hunt, however, decides to tread a different route. Each ghost/spirit/curse comes with a mystery that has to be carefully unravelled, usually with many mishaps and false assumptions along the way. There's a lot of detail on Japanese myths, folklore, customs and rituals that the characters toss back and forth amongst each other in an attempt to pinpoint the nature of the ghost they'll be hunting and the method of banishment they should use. The plot as pertaining to the supernatural always takes centre stage, so if you're the type of person who doesn't like using their brain for manga, do yourself a favour and read Tasogare Otome x Amnesia or something of that ilk instead. Personally, I found the numerous titbits on Japanese superstition enhanced my reading experience and understanding of the plot, especially since I had little prior knowledge on the topic.
(2) "The supporting cast is boring and has no depth. Also, the relationships between them are underdeveloped."
I found the supporting characters immensely entertaining, myself, but there is some truth to this in that none of them (except Kazuya, and he's a main character) have interesting backstories or any particular motivations behind their being in the business. Their motives for helping Mai and Kazuya are usually either "We felt like it, so we did," "Well...we're sorta friends, right?" or "This case is way too interesting/unusual/high-profile to not have a hand in." Imo that's more believable than all of them falling in love with one another or having being tormented by spirits themselves as children, but if you're expecting things like multiple pairings (especially since all the recurring characters are quite attractive), you might find their generalised friendship-cum-teamwork-cum-business partnership boring.
(3) "Mai's an annoying brat and Kazuya's the stereotypical "cold male lead" of mainstream shoujo."
Both true, except that in Ghost Hunt they are the way they are because of their pasts, upbringing and experiences -- all of which are related to the plot in one way or another -- and not merely to create romantic/sexual tension. I have no issue with Mai, because she strikes me as a lot more realistic than your run-of-the-mill shoujo girl in that she's neither an unattractive crass tomboy nor a perpetually-blushing Shrinking Violet, but something in-between: one minute loud and childish, the next moment quiet and considerate, and in yet another moment fangirling over "Naru." I wasn't particularly drawn to Kazuya as a character or as a person, but his intelligence is very consistent (in the sense that he doesn't inexplicably become stupid when the love story or the plot tosses the Idiot Ball at him) and his coldness is relevant to his personal history, abilities and motivations, so no complaints there, either.
(4) "The romance is unresolved, so the entire story was pointless!"
Considering how slowly it was built up and the added complication of "other Naru," I can't understand how anyone could have expected anything different. A rushed HEA would have been unfitting (to both the plot and the two MC's personalities and circumstances) and unnecessary, as they were obviously saving the resolution of the UST for the sequel. Not that I approve of such blatant sequel hooks, but in this case it was quite fitting.
As for whether the lack of an end pairing makes the whole thing pointless or not... While Kazuya/Mai is, in fact, the only serious relationship in the story, Ghost Hunt is unusually plot-centric for a shoujo manga, so if you came here looking for a prominent romance, you're going to be disappointed. Every tag in the genre field gets just as much focus as the love story, so apart from "supernatural horror," no other genre predominates.
(5) "The ending was rushed."
The way I see it, most of the people who complain about this are referring to the unresolved romance/emotional aspect and not to the rest of the plot, which was being built up practically from volume one onwards. The conclusion could, admittedly, have been smoother, but an author struggling with the last volume -- especially when having to pave the way for a continuation -- is nothing new, and not a reason to refrain from reading, imo.
All in all: not a flawless series by any means, but a very entertaining and reasonably intelligent (especially considering its target demographic) read.