Okay, so I've been digging through Alaskan newspapers and so far I've discovered that the national media knows little about this issue. Here's what I found:
The problems began when Palin fired her Public Safety Commissioner, Walter Monegan. Monegan failed to adequately fill vacancies in the state police (upwards of 50-60 total slots) and varying sources suggested difficulties in recruiting as a reason. In addition, Palin discovered that Monegan had gone directly to the State Legislature to request additional funds for his department without her approval. These funds were not authorized by Palin and, in fact, violated her strict budgetary requirements. As a result, Monegan was fired. Monegan never claimed lack of funding as a reason for failing to fill the slots and the legislature refused his request, citing his inability to fill the vacancies as evidence of incompetence (in so many words).
As Governor, she has the authority to do this and no one disputes that.
Shortly after the firing, a blogger named Andrew Halco, described as a "former political rival and relentless critic of Palin's" looked into the firing and eventually conducted a private interview with a Trooper named Mike Wooten, who Halco knew was once married to Palin's sister and whose marriage ended in divorce with a bitter child custody fight. These things had been well-publicized by the press and occurred before Palin took office as Governor. After Halco's investigation, the Alaska State Trooper's office released Wooten's file to the media and it should some nasty stuff. During this divorce, Wooten was suspended for threatening to kill Palin's father, for tasering (yes, he tasered) his 11 year old stepson, for drinking beer in his squad car and for violating wild game laws. The suspension was for 10 days and was later reduced to 5 days after a union protest.
Apparently, Halco claims that Monegan was fired for failing to fire Wooten under pressure from the Governor. Monegan was silent on the issue for a lengthy time. Palin's office refused to comment on the firing as well, out of respect to Monegan (so they claimed). But once Monegan broke his silence he began openly discussing the firing, and claiming coercion. Palin's office then released the details and the reasons behind his firing.
Monegan claims that Palin's office contacted him many times to exert pressure on him to fire Wooten. Records show dozens of calls from Palin's office to Monegan's, but these have all shown to be related to appropriate day-to-day business, except for one where there was a somewhat suspicious conversation. In this conversation, a man named Bailey (from Palin's office) was discussing a routine matter with Monegan when the topic drifted toward Wooten. Bailey was on tape saying (pp): "Sarah and Todd are scratching their heads as to why this guy is still on the force, he seems like a huge liability when it comes to recruiting".
Palin claims that she was unaware of this conversation and never authorized Bailey to discuss Wooten with Monegan's office. As a result, Bailey was suspended for an unspecified time. When Palin was made aware of the tape of the discussion her office immediately turned the tape over to the AG's office and formally requested that he open an investigation into the matter. In addition, the State Legislature, under Republican leadership, also enlisted the services of an independent investigator and began immediate chatter about impeachment. Related or not, it's important to understand that this is the same legislature that Palin was at odds with regarding fiscal discipline and ethics reform. To say their relationship was strained would be an understatement. Palin, while popular with the people, was NOT popular among state politicians.
To this point, that one phone conversation is the only evidence of Monegan's accusation. No one else at the Dept of Public Safety has complained about the Governor's office or claimed coercion. Monegan has also complained about not receiving a pension, although he technically was not fired but was offered a different position outside the area of department head, or basically offered a demotion. Monegan refused and thus, technically, resigned his office.
So you can form you're own opinion, but I don't see this going anywhere. Yes, this one statement was somewhat inappropriate but Palin's response was adequate. It does not represent enough evidence of Monegan's claim. Granted, more evidence may emerge and if she is found to be abusive of power then, obviously, she should resign her nomination. It looks like Halco made quite a large leap in connecting this story and coming up with the allegations of coercion, but that's just my opinion. McCain doesn't seem to be concerned about this, so this probably won't go anywhere.