The "Ribcase" acronym came along with the improved gearbox installed in most later '60's and '70's Sprites and Midgets, to go along with the bigger engines. The original "smooth case" design was conceived around small displacement low torque and horsepower engines, the 948 and 998 as used in Spridgets and the early Morris Minor. The demands on this gearbox were well within design limits. Over the years the engines got bigger, as did the weight of the cars they were installed in. Not only was it necessary to upgrade the internals, etc to take all of these loads, even the external housing had to be strengthened- thus a 'ribbing' was cast into the main body of the tranny and it has been called the 'ribcase' ever since.
The Ribcase has been produced in the hundreds of thousands, and found itself used in more applications than ever envisioned. From the very simple demands of a light weight street car, it has now been used in race cars of all sorts with enormous amounts of power. Every weak link with the original design will be found when subjected to such abuse. The average street driven gearbox actually suffers from all of the same problems. It simply takes longer for them to show.
The most common problems with the ribcase have to do with the reality that the gearset was designed with only 3 syncro rings, and thus first gear takes abuse even with the most conservative drivers. A first gear 'wine' is obvious due to it being straight-cut. As bearings and shafts wear, it is matter of how loud it gets before it will start to also distroy the counter gear on the laygear, and it's bearings and shaft.
In recognition of the age of any Ribcase (the vast majority were built more than 40 years ago!), is it very unlikely that you can find a box that someone has not done a "quick and dirty rebuild" on sometime in it's past. For a number of reasons that all stem from inexperience- the problems result in the transmission 'popping out of 2nd gear' during deceleration.
The third most common problem is simply a matter of reality exceeding design limits of the layshaft and bearing. The 'counter-gears' or laygear is the shaft that carries four gears and transfers loads as the gears are shifted. This hard working assembly was designed to spin on a simple straight shaft with only two small roller bearings as support. The laygear bearings and shaft simply are not prone to long life, particularly with powerful engines, and should be replaced EVERY time the gearbox comes apart for any reason. If they are allowed to degrade too far before replacement the laygear it self will also need to be replaced. The only outward sign of this internal problem will be a very small amount of increased rumble as you drive the car, until a complete failure becomes obvious.
The fourth most common problem with the ribcase are the synchro rings wearing out, resulting in grinding gears when shifting. Easy to check and easy to replace, and much less expensive than the labor, it just makes good sense to replace them EVERY time the box comes apart. The symptom of synchros wearing is simply that it gets increasingly difficult to change gears without hearing just a little crunch (that gets worse) as you shift.
The fifth most common problem is the self destruction of the pilot bearing that locates the 1st motion shaft onto the main gear cluster. Fourth gear is carried on the 1st motion or input shaft, and into it rides the main or 3rd motion shaft, located by a very small roller bearing that keeps things centered and takes all the load. As this bearing degrades it will also destroy the surface hardening of the shaft, with resulting devastation to the increasingly rare and expensive main shaft. Early on, you will not really be able to tell anything is wrong. As it gets worse, shifting between 3rd and 4th gear will become increasingly difficult.
Frequent oil changes with a visual inspection of the old oil (and the magnetic drain plug) will go a long way to serve as an early warning of brewing problems, and minimize the potential damage. Be SURE to use standard 30wt engine oil in the Ribcase transmission! 90 weight gear oil will result in rapid wear of the synchros.