Were/are there people who genuinely believe Nixon didn't do anything wrong, besides Nixon and his closest advisers?
/u/The_Alaskan 's response about Nixon's support during the Watergate Scandal might help to answer some of your questions:
Yes, I know some of them. Let me explain in the specific context of an organization/institution I've had some interactions with: The Richard Nixon Presidential Library.
The Richard Nixon Library was built in Yorba Linda, CA and opened in 1990. The federal government of the United States normally operates Presidential Libraries. They provide federal funding, send materials for safe-keeping to the libraries from the National Archives, and generally involve themselves in the administration and upkeep of the Library. When it came time to build the Nixon Library, the federal government opted not to involve itself. They refused to sanction it. So, instead, the Nixon family set about building their own library and in order to do so they raised 25 million dollars completely from private sources for its construction. That would indicate that there were plenty of Nixonians out there still eager to support the President. But there's more going on. In order to staff the Library, which was operating on a pretty tight budget given its lack of federal funding, the administration essentially incorporated an extensive system of volunteer docents, usually (but not exclusively) upper/middle class white elderly individuals, almost all of whom were universally Nixon supporters. In 2004-2005, the federal government finally authorized the absorption of the private Richard Nixon Library into the federally-funded and directed Presidential Library system. This, in turn, caused some significant consternation among both volunteers and other supporters of Nixon for fear that the National Archives would, in their administration, change the Library to a fundamentally negative portrayal of Nixon when it had been giving a relatively positive description of Nixon up until that point. Similarly, the National Archives were concerned that the Nixonian loyalists would essentially put up a constant struggle for control of the workings of the Library in order to maintain a distorted, intentionally rosy view of Nixon. Historian David Greenberg was quoted as saying, "“With Nixon, there is such a history of distorting history that one has to be suspicious of whether the Nixon family or loyalists will continue... Even though we trust (the) archivist to do things honest and fairly, there are ways.” One real sticking point was the private Nixon Library folks wanting to cancel an annual conference on the Vietnam War when it became apparent that the anti-Nixon attendees would outnumber the pro-Nixon attendees. The National Archives basically had to step in and say, you can't do that, reschedule the conference. Things like that essentially have gone on for quite some time since, until relatively recently when the Library got a major overhaul and a lot of the loyalists were essentially either no longer involved or had passed away, now it's a relatively fair and balanced portrayal of Nixon's presidency.
Long story short, there were plenty of Nixon supporters who were actively involved as both volunteers, donors, and administrators at the Nixon Library both in its private and federally funded incarnations. My high school girlfriend's grandmother was actually a relatively high-level volunteer/coordinator for the docent program and was herself a Nixon supporter and thus knew a large number of Nixon supporters who I had occasion to meet at a number of social events. They tended to stray away from talking about Watergate (keep in mind I was in high school at the time, so I wasn't really able to engage them in the kind of conversations I would be able to as an adult now) and focused on the most positive aspects of Nixon's presidency. When pushed, I heard a number of them express the idea that Watergate was overblown or a political hit-job, despite Nixon's wrongdoing. I had similar experiences interacting with many of the docents at the museum (to this day, I was there not long ago and there's still plenty of elderly pro-Nixon docents hanging around). They are out there and they are very supportive/protective of a man they believe to be a good President brought down by his enemies rather than his own flaws.
Sources:
Personal experience
http://www.latimes.com/la-oe-greenberg9jul09-story.html
http://www.ocregister.com/2006/01/26/nixon-library-joins-the-fold/
Bonus content: Hunter S. Thompson's obituary for Nixon, a must read political piece imho: https://www.theatlantic.com/magazine/archive/1994/07/he-was-a-crook/308699/
Edit: I should clarify that the "despite Nixon's wrongdoing" is my own interjection, because, objectively, Nixon did bad things, there was a reason Ford had to pardon him. The people that I knew who were Nixonians almost entirely believed he didn't do anything wrong or, in a push, anything another President wouldn't have done in his position. Rather, they felt he was unjustly brought down by his political enemies and devious detractors. The original Watergate exhibit at the Richard Nixon Library tended to significantly trend that way.
Follow up question if I can. I've always read that Nixon was a valuable surrogate for Ronald Reagan during his electons. Is this because enough time had passed that people forgave him, or was he reaching out to a group that never thought he did anything wrong in the first place?
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