I'm just going to hit these in order:
Needs fixed, but can be done with minor tweaking.
Keep the current bowl system intact, but create a four team playoff based on the top four BCS teams (Final Four). The semi-finals can be played New Years Day while the championship follows the week after.
I think paying players happens more than what people think and even by schools you wouldn't think of. The coaches may not be directly involved but there are boosters who can bring down a program.
Paying Players and Amateurism
The players should get a larger stipend. You can point toward getting an education for free, but in todays job market graduating college does not necessarily equate to landing a job in your field. I think it should be set up similar to a COD where the students aren't allowed to touch the money while on campus, but upon graduation you've got a safety net available.
See the point I made above on how IMO it happens more than people think. Some of the rules are absolutely ludicrous though and need to be changed such as chanting names of recruits at a Midnight Madness.
I don't like it, but I'm not against it and I would like to see the NBA adopt the MLB system. You can enter the draft out of HS, but if you elect to attend college, you must wait until your junior year.
OTOH, college today is not the same as college 10 years ago. I mentioned Michael Kidd-Gilchrist in the UK thread as to why he should go pro, but consider with how hard he plays physically that he is very susceptible to injury and needs to get into the league instead of possibly suffering a major injury in college and costing himself millions.
The same opportunities for degrees are available online. I'm taking three e-courses and an Alternative Delivery (once a month) class next semester at a community college here in Parkersburg. I imagine the e-course route is available for students at major colleges as well. I remember where Vince Carter returned to UNC to graduate after leaving early for the draft so it can be done.
The Arkansas situation wouldn't surprise me if one of two things happened:
Bad Behavior by coaches (see Pitino and Petrino)
1. Petrino is fired.
2. Petrino is allowed to keep his job because "he wins" and the AD doesn't sugarcoat it.
If a coach does something embarrassing to the university and in most cases, a flagship school for the state and community, the coach should be fired or asked to resign. If a player does something shady, that player is likely dismissed from the team and loses their scholarship. Coaches are some of the states highest paid employees and should be held to a higher standard.
You can include Syracuse here as well. As an outsider, its obviously deplorable. From somebody living within the State College community though, I'm sure people within the community have different feelings toward Paterno, Sandusky, etc.
Whatever happened at Penn State
I posted this in the Penn State thread before, but there was an area coach here who was banned from coaching in a similar situation. Depending on who you talk to around here though, there are people who get downright defensive when you bring up about this coach and swear that he didn't do what was alleged but that it was all brought about by a disgruntled former player.
What makes the story even more incredulous is that this same coach had a contact with a former Penn State coach who conducted camps here in the area. Some of the players here in Parkersburg went to Penn State during the 1980's. Wanna guess who the coach was?
As reds1869 said, both are necessary evils. TV deals though are ultimately going to go the way of cable networks.
Money in the system (Boosters, TV Deals, etc...)
Point Shaving scandals (every few years)
The NCAA is a corrupt and hypocritical organization. They are more interested in making money off their "student athletes" and that made it even sweeter to watch Mark Emmert hand the National Championship trophy to John Calipari last week. I've said before that even if the NCAA ever vacates Kentucky's national championship, the end result is that Kansas still lost and the fans still remember the joy felt after watching their Cats win it for the first time in 14 years.
NCAA rules and many many more.