tl;dr : Saul Goodman committed a LOT of crimes in Breaking Bad

Saul has a personality disorder and it's interesting to watch it manifest in Better Call Saul.

What personality disorder is that?

I'm no psychologist but 

The dark triad is a group of three personality traits: narcissism, Machiavellianism and psychopathy.[1] [2] [3] Use of the term "dark" implies that these traits have malevolent qualities:[4] [5] [6] [7]

• Narcissism is characterized by grandiosity, pride, egotism, and a lack of empathy.[8]
• Machiavellianism is characterized by manipulation and exploitation of others; a cynical disregard for morality, and a focus on self-interest and deception.[9]
• Psychopathy is characterized by enduring antisocial behavior, impulsivity, selfishness, callousness, and remorselessness.[10]

All three traits have been associated with a callous-manipulative interpersonal style.[11] A factor analysis carried out at the Glasgow Caledonian University found that among the big five personality traits, the trait of agreeableness is strongly absent in regards to the dark triad, while other traits such as neuroticism and a lack of conscientiousness were associated with some.[9]

http://en.wikipedia.org/wiki/Dark_triad

Wow, I had never heard of that before. Does he really become a psychopath?

The other two I can see, but he is less impulsive and more remorseful, even late in Breaking Bad.

He's the voice of reason.

"Conspiracy to commit murder" seems psychopathic to me.  (Buried and Rabid Dog)

Do you think Walter White possessed all the dark triad personality traits?  I do, but even he tried to save Jesse and provide for his family in the end.  

Yes, Walter White is impulsive and remorseless. "I liked it. I was good at it."

But Saul Goodman is always trying to get people to not kill people.

He was the voice of reason in Buried and Rabid Dog. He tried to de-escalate.