Hey what makes you say DMC4 was rushed?
Last time I checked they announced they were working on it in 2005 (same year DMC3 SE came out) and the game came out in 2008(finished sometime in 2007). So they had at least 2 years to work on it (not 1).
http://www.youtube.com/watch?v=Uy1uc_CVjh4
If anything the devs just wasted a lot of their time or got lazy.
You can examine in the TGS trailers to see how it was progressing and by 2006 they decided to go the Nero route (the current route).
Considering in this one trailer they literally had dialogue that was used at the end of the game meant they were either almost done or the voice actors just finished their part.
As for being an incomplete game this game had more than 2x development time DMC2 had and DMC2 managed to not have the issues DMC4 has (backtracking) but still suffered some of its own problems.
However, the main problem of the game's development can still be traced back to Kobayashi. Early trailers indicated that when starting DMC4 Nero wasn't on the dev team's mind.
What happened?
Kobayashi
Kobayashi was the one who wanted a new main protagonist (Nero) and wanted to make DMC4 more appealing to Japanese female audience (also males too) and thus introduced the sappy love drama and Kyrie.....oh yeah and Nero. Plus made it more animeish....like a bad bishonen.
Whatever original plans Itsuno and the other guys had were scrapped by their producer......Kobayashi.
The higher ups didn't do much to anything to negatively harm the development process other than gave them a fair time limit (you guys have now in 2005 up to mid to late 2007 to finish this game....a fair 2 years) and even gave them an extremely high budget too.....super high.
They could've extended the development time or delayed the game like DmC but it may have been a marketing thing plus it was apparently Capcom's first game developed on this current gen consoles so they didn't want to stall time (be honored Capcom chose DMC as the first game they decided to enter the new gen with).
As for the writing and story....the same guy who wrote DMC3 (Bingo) was the main writer but this time he didn't had Takayasu with him. However even DMC4 seemed lazy or sloppy for him considering he wrote DMC3 & the DMC3 manga both had pretty good, mature, and dark stories and plot and it seemed with him DMC was going somewhere....so what happened?
Kobayashi
Kobayashi felt a more anime style...no even the past DMC felt a bit animeish.....Kobayashi wanted to make DMC4 into a bishonen or bishojo to appeal to more Japanese female audience. Did it work? DMC4 is the highest selling DMC game in Japan with over 500,000 units..............it worked sadly....No I'm not upset Kobayashi's plan succeed more power to Capcom I'm upset that its another hint that the Japanese are a bit shallow or buys into stereotype (OMG NERO IS SOOO CUTE MUST BUY!!!! HE AND KYRIE ARE SO KAWAII!!! DANTE IS SOO FUNNY AND COOL HE IS LIKE A ONE PIECE CHARACTER....please put a bullet in my head)....Its not the first time I questioned the Japanese consumers decisions.
On a side note Kobayashi also was part of the DMC anime and that sucked too....okay it was decent at best.
As for why the story is so bad (or I would say plain or poorly well constructed)....despite being a run of the mill D-class Shonen it had potential to at least to be an interesting story and work out well.....but what happened?
Inconsistencies, no character development if there was it was shallow as all hell (Kyrie), fan service up the wazoo (Lady and Trish), lack of backstory/explanation (they only explained the Order's origins and how Sparda tied in like a paragraph, more info on Nero please, where are Kyrie's parents, why can Yamato open and seal the Hell Gate, who made the Hell Gate or how it got there, what demons did those Devil Arms originated from, and most of all how come Nero has a demonic arm while Dante and Vergil don't), useless moments (Gloria's/Trish's role...she might as well as not been in the game if that is all she does) Dante being retarded (fanservice probably), and forced plot devices that just makes the story looks laughably bad (Trish giving them the Sword of Sparda so she can gain intel but in the end doesn't gain any intel or do anything relevant outside helping the bad guys....sure Dante addresses this and Trish didn't give a damn and its probably due to her being a demon but she did care enough to save the civilians but it makes her look even more bad first she was skanky eye candy but because of that she evolved into stupid b*tch, DMC4 managed to discredit all of the females in DMC except Lucia). Plus anything they did explain it was so faint I had to use wikia to understand it like those Devil Arms you got after beating a boss were the same Devil Arms Lady was talking about. Heck in my first playthrough I didn't understand half of what the hell was going on.
I don't know what Bingo did but it obviously wasn't him since he wrote DMC4 Deadly Fortune (which is a more better and proper version of DMC4's story it explains everything about Nero, Kyrie, the Order, and much more on the game's story to the point I wished Capcom made a special edition or Expansion game (eg: Ultimate MvC3, Super Street Fighter IV, Dragon's Dogma: Dark Arisen, and Dead Rising 2: Off the Record) using that game's story.
The game wasn't rushed it was poorly done and its not hard to believe considering Itsuno's team has f*cked up before.