I'm going to take one more stab at this after researching for a while. Please leave comments and vote based on whether you think this is plausible or unlikely.

I am accusing Alex Jane as being Red John. I will keep this short and to the point. Here are my reasons (both in the story and from the cast and crew's point of view):
1. Red John is much like Patrick and it is possible that he could be Patrick's former teacher i.e. his father Alex Jane.
2. The episode in which Alex appears, 'Throwing Fire' was partially written by Bruno Heller himself. Bruno usually works on all episodes regarding Red John himself.
3. Alex Jane could have known about Patrick Jane's 'happy memory'.
4. Alex has motive, when Patrick Jane ran off with his wife from the carnival, it is said that his father was enraged. He could have taken revenge on Patrick by killing his wife and daughter.
5. Bret Stiles says he knew Patrick's father, it has been established that Red John was in Visualize long ago. This certainly fits the time frame, as the first Red John murders took place in 1988 and Patrick and his wife left the carnival in 1985. Thus, his father could have been there in 1988.
6. Alex Jane is portrayed as a master manipulator. This could stand as reason that he could gain influence over people in the FBI and CBI. 
7. Alex wears a wedding band even though we never hear of Patrick Jane's mother. Red John, as previously seen, wears one as well even though it seems he could be unmarried. He wore it while having a 'relationship' with Rosalind at least.
8. In the episode 'Red John's Rules', Alex Jane is brought up again as a topic of conversation, Sean Barlow mentions that Alex is a wicked man that exploits others. Red John is obviously a wicked man as well.
9. It is mentioned on many occasions that Patrick and Red John know each other extremely well. How much better can two men know each other than a father and a son.

As far as I am concerned, the only possible flaw in the story would be the handshake comment. Why would Patrick only become friends with his father when they 'shake hands'? That does not make much sense.

However, I feel that Patrick's father fits the clues and I like him for being Red John. I do not believe he works alone, but he is in my opinion Red John.

Please comment. I would like to know if I am missing something that would exclude Alex definitely. But please do not dismiss this without evidence.