As for the rumours, I have no idea if they dated and broke it off after the show, but during a special (or something) to do with the movie, he seemed to be happy for her success.
Also, she appeared as a guest on Arashi's variety show, and things seemed to go well then, too.
As for Shun Oguri, during the same special, he said he was 'touched to have been able to talk to her so naturally after being so nervous when he was younger'. Also, they look like they get along well in some pictures from the movie set.
Sorry for the long post!
They dated in 2002 because a reporter caught MatsuJun driving Yukie home to her apartment around Dec 2002 (Jun mentioned on Hanamaru Cafe that he got his driver's licence in Oct 2002 and bought a car in Nov 2002, so it makes sense). Throughout 2003 until 2005 they were spotted going out to romantic dinners a lot, watching kabuki and butai plays together and other sightings, even though paparazzi never caught any pictures of them together. He was also often seen visiting Yukie's apartment building during that time.
I think they broke up in 2005 (the sightings of them together ceased after 2005), and apparently it was a difficult breakup because he declined to act in Gokusen 2. And about Jun and Yukie's fight affecting even people close to Jun... I've read a rumor in a Japanese website that Nana Eikura (Jun's rumored girlfriend back in 2008) quarreled with Nakama Yukie about Jun. It was around the same time the 24Hr TV was being under preparation, where Arashi had to work together with Yukie as hosts of the show. Nana wouldn't allow Yukie to come close to Jun, or something like that. I've also read about Shun being awkward around Yukie as well...
As for whether he has finally moved on, I think he has. I assume that him hosting 24Hr TV with her sort of patched things up, because after that he did that video tribute thingy to Yukie for the Gokusen movie (he still didn't act in the movie though, I think it was because he was busy with Smile and Arashi's 10th-year-anniversary) and she made an appearance in Himitsu no Arashi in 2011. In the industry, being on-screen together with a past rumored girlfriend automatically means that there is nothing between them anymore. So... yeah.
Besides, he's been talking about marriage a lot recently, so I'm sure he's in a happy relationship right now.