The bad name may come from use as a dg rifle. Cartridges sticking in the heat I believe. Not a Mauser Action. Those sort of things.
The flip side of that is the MK-V is the slickest feeding DG rifle of all time due to it's straight line feeding from a single stack magazine, and handloads takes care of sticky actions in the heat. Areas where I think there were honest criticisms were with the 9 lug action and in some cases too light a contour barrel. In the early days before CNC machining, it was very difficult to get equal bearing on all 9 lugs. Consider for a moment how many two lug bolts have shiny rub marks on just one lug, or heavier rub marks on one lug than the other.
The barrel contour particularly of the 26" .300 Weatherby, made it very whippy. Now the logic was plain enough, a 26" barrel got the most out of the overbore cartridge, without needing to add wheels and a lanyard to the rifle, but a heavier barrel would have ruined the balance, making it too muzzle heavy. Related to the light contour barrel, is the accuracy question. Deservedly or not, The MK-Vs were frequently criticized for being less than tack drivers. Part of the problem might have been the long bullet jump that Weatherby machined into the lead as another velocity enhancing technique, making it impossible to minimize the bullet jump with rounds that were fed from the magazine. I doubt that accuracy was as bad as was often reported, but the following example is from my own experiences.
I was at the range one day with my M-700 ADL in .30/06, with a cheap Bushnell 3-9X scope in Weaver mounts. At the next bench was a fellow with his MK-V in .300 Weatherby with a Leupold scope, but I don't recall what mounts he had, it was a long time ago now, perhaps they were Conetrol, and his rifle was resting in a very nice benchrest. I was shooting off sandbags. I was impressed with his outfit, he had those expensive C-Clamp style micrometers to measure case head expansion, and he busily wrote stuff down after each shot. It was only a 100 yard range, so neither of us had the opportunity that day to stretch the legs of our rifles, but at a pause in the shooting, we wandered down to check our groups. Typical for my rig, the group was about .75" from a 165 gr Hornady over a compressed charge of Ammo Mart 4831 equivalent powder. His group was an inch bigger. When we got back to our benches, he asked what I was shooting, because he found my muzzle blast objectionable. So his accuracy while sufficient for big game hunting, wasn't the sort that induces excitement from a rifleman. So what was behind the Weatherby's poor showing? Too light and whippy a barrel, uneven bearing surfaces on the lugs, too long a lead, or just a shooter upset by the muzzle blast from my rifle?
Some years ago, a particularly gunny South African doctor here procured a MK-V in .30-378 topped with a 16X MK 4 Leupold. At a half mile, he rang the steel plates much easier than I could with my .308 target rifle, a tricked out 700. Oh yes, there was a 60K full value cross wind blowing, driving horizontal rain. No problem with the accuracy of that Weatherby, even under miserable conditions. Could have been just a tighter nut behind the trigger.