We would like to install a half bath in our finished basement in Colorado. The issue that I seem to have is that the ceilings are short at only 73". My understanding is that code requires the ceilings to be 80" in front of the fixtures. We can't do anything about the ceiling height, so does this mean that a bathroom wouldn't be an option in our basement?
It may be possible to be granted an exception regardless of what code states depending on the flexibility of the Authority Having Jurisdiction.
Ask the Authority Having Jurisdiction. In other words, ask your local building department or whomever has authority to approve permits where you live to see what they require and whether they would permit such an exception.
For example: When I was finishing my basement, I have a point that goes below minimum required ceiling height for my state's building code. My local building department follows my state's building code. My state's building code is generally based on the International Residential Code, but has a few exceptions (one noted difference in my state is the required minimum height for finished ceiling heights and protrusions when finishing pre-existing unfinished basements). My building department granted me the exception I listed in the submitted plans. This example also shows exactly how locale-specific this question is.
I don't think that means a bathroom isn't an option, more that it's considered a "non-conforming" bathroom which may or may not count in potential listings for sale.
If we go off of my local code (2012 IRC), the minimum ceiling height is 6'8" (OP mentioned this with their 80" comment). Looks like you're just 7" short.
Now, if this is because of a beam or other obstruction that isn't normal ceiling heights, looks like you can lower that requirement to 6'4" (according to 2012 IRC), but that's still 3" too short.
I'd be willing to bet the space, although probably nice and definitely a bonus, is really just all non-conforming basement area, regardless of what else is down there, due entirely to ceiling height.