There's been discussion in another thread about the differences between may issue versus shall issue when it comes to concealed carry.
Tennessee Gentleman ("TG") had commented on may issue and how much some States might actually have, for all intents and purposes, a shall issue procedure even though they call it may issue.
All I can say is how it is in Michigan where I live.
In Michigan, the State has to allow you a concealed carry permit as long as you meet objective requirements.
One of those areas involves a laundry list of infractions that you cannot commit within a certain time period before applying for the concealed carry permit.
This laundry list of infractions is about as long as your arm!!
Anyway, there are 3 year and 8 year categories of prohibiting infractions in Michigan (along with lifetime prohibitions for the usual more serious infractions, plus insanity).
Here's the link to the Michigan application, go down a few pages to where the infractions start.
http://michigan.gov/documents/ri-012_7736_7.pdf
In answer to TG's main question: In Michigan, LEO does not give their personal opinion. The laundry list of infractions covers the prohibitory objective standards for shall issue in Michigan. You meet those standards and the State
shall issue a concealed carry permit.
ETA: Now the authorities do investigate you via background checks with the FBI and State/Local criminal records. You are fingerprinted and the FBI runs a check on those prints.
As stated, all of these requirements are objective in nature and, if you meet them, the State
shall issue the concealed carry permit.