I have two Ruger No. 1's, one in .243 and another in .30-06.
With factory barrels and no additional work, the .243 did 1" groups and the .30-06 did 1-1/2 to 2" groups at 100 yds. The .243 had acceptable headspace and the .30-06 had excessive headspace.
Rather than fight with Ruger, I decided to take advantage of the opportunity and have custom rifles built from these.
After replacing the barrels, bedding the forends to the spring hanger and receiver (which free-floats the barrels) and some trigger work, the .243 now does 7/8" groups and the .30-06 does 1" groups. I'm still working up loads, but I'm happy with the results of the custom work.
Because the barrels had a different contour, I had to lap the rings to get the scope "centered" (parallel to the bore with both turrets zeroed).
Ruger No. 1's can be very accurate out of the box, but I believe there is no guarantee that any particular rifle is going to be a 1 MOA rifle. Ruger's accuracy standards are pretty loose...I think if you get one that shoots 4" groups at 100 yds, they might
As far as reliability, there aren't a whole lot of moving parts but they have to be kept clean and lightly oiled. The No. 1 is harder to disassemble than a bolt-action, but an annual strip to get at the internals isn't too difficult.
The only real advantage the No. 1 offers, IMO, is that it is very short overall for the same barrel length. There just isn't any "receiver" behind the barrel.
However, this advantage also makes scope selection challenging. I've found you need either a scope with 4" of eye relief or offset rings to position the scope where you don't have to "crawl the stock" to get a full sight picture. The ring location just isn't "conventional", compared to a bolt-action.
While the difference between a Zeiss Conquest and Leupold VX-II isn't much if you just look at brightness and clarity, the Zeiss has that extra 0.5" of eye relief.
Finally, the Ruger triggers are not adjustable, and after-market choices are limited and/or expensive. Someone who is familiar with Ruger triggers can improve them, but it isn't recommended for the kitchen-table gunsmith.
So, the Ruger No. 1 is a good rifle. But it has issues that are unique to its design.