We work primarily in the historic districts, with single family homes, so are very familiar with HDRC. Their main focus is to make sure the exterior remains historically accurate. Things like siding and roof, windows and doors, porches and fence. Each historical neighborhood has it's own set of guidelines as to exterior paint colors and landscaping, but those can easily be navigated with proper paperwork to receive an approval letter.
Other things to look for are foundation, water damage to sub floor in kitchen and bath areas, lack of insulation, etc. You're right on plumbing and electrical and that is typically two of the biggest areas of concern. We work with investors on flips, so the level of rehab detail is more than what you would need for buy and hold.
My wife and I are investors, but also work with the investing community on historical design projects. Feel free to message me if you want to discuss further.