I'm thinking post-TAHITI. From what I can tell, his actions have only been in SHIELD's best interest.
I think he is SHIELD.
But the members of "the real" SHIELD seem to think he is not.
Coulson's loyalty has always been to SHIELD, unwaveringly as far as we've ever seen (with the sole exception of his crisis of faith after learning about TAHITI).
That being said, there is one group who claims otherwise...
The "real" SHIELD
However, so far they haven't outright accused him of doing anything specifically disloyal, more that they simply don't trust him due to the effects of TAHITI and his subsequent actions.
A few examples:
...and most importantly...
The organization in question points to these facts as evidence that Coulson may have been altered, impaired, or otherwise changed from his TAHITI experiences, and as such may not be capable to lead SHIELD. The final point explains why they didn't simply contact him about it, and felt the need to work against him (or at least keep him under surveillance) without his knowledge.
Put simply, they're not doubting his personal intentions, so much as they're doubting whether it's a good idea to put a PTSD-suffering, obsessive-compulsive alien-blood-experimentee with trust issues and questionable allies in charge of a global intelligence and military organization.