The first two things I would want to examine are the method used to set focus in the camera, and what is being done to avoid vibration problems.
It appears the camera is mounted directly to the microscope. This can make vibration problematic. One way to "eliminate" it as a problem is to put neutral density over the light source and use exposures of about 3 seconds or so. Any methods the camera provides to reduce vibration, such as mirror lock-up, should be used. (I don't know too much about this camera, but generally it's really tough to use a SLR directly on a microscope if it doesn't have -at least!- provision for avoiding mirror vibration).
As to focus... naturally it is very critical. Many are not aware that it is not a good idea to focus the camera image by changing the microscope focus to the point it is no longer in focus through the microscope eyepieces. When this is done, you "upset" the objective-to-subject distance for which the objective design was calculated. (In truth this is not a big issue with low mag/low NA ...numerical aperture... objectives, but it is not a good practice). When people use a manufacturers dedicated camera system that was designed to be used with their microscopes this is not an issue since it the camera is made to be par-focal with the eyepieces (or extremely close to that ideal). When you "adapt" a camera such as a SLR, it's always a good idea to try to make the attachment in a way that the camera can be adjusted up/down so that it can be made par-focal with the eyepieces.
An absolutely vital piece is the "low-power, projection eyepiece" used in the trinocular head. Your acquaintance says that he used the "K4:1". The "K" part is important, because that means it is properly "corrective" for the microscopes objectives used. (Most microscope objectives from this era were designed so that final color corrections were made via an eyepiece... either a "visual" one or a "photo" one. These are usually marked with a "K" or "C"). One red flag I see is the magnification. A 4X relay magnification is really too much for a 4/3 sensor. An appropriate relay magnification for a 4/3 sensor (format diagonal of 21.6mm) would be in the range of 1.25X to 1.5X. A relay magnification of 2X would be "usable", but at 4X you are recording a highly magnified section of the center of image formed by the objective. (The recorded image would be only about a 5mm diameter section of the 20mm diameter image formed by the objective). An analogy --not perfect-- would be to consider the image quality you might obtain if you put two 2X "teleconverters" on a regular camera lens. You'll get a "bigger" (more magnified) image, but I would not expect too much in terms of resolution or image quality. With a microscope image it's even worse, because the physics of light (i.e. "diffraction") causes the resolution you are starting with to be already fairly limited (low). Enlarging this too much results in what is commonly referred to as "empty magnification".
I can't really offer a good solution to this. When these microscopes were made, 35mm was about the smallest format to consider (24x36mm with a diagonal of 43.3mm). The typical "low-power, projection eyepiece" made to be used with the 35mm format was between 2.5X-3.3X. (And again, the 4/3 sensor has a diameter that is only half that of the 35mm format). Lower power relays can be purchased from third party manufacturers, but they are very expensive and would not have the proper corrective capabilities. One thing that can be tried is to "raise" the photo-eyepiece in the trinocular tube. That will reduce the magnification it provides. The camera will need to be moved to make things parfocal again. This is not that difficult, but it does require some custom work.
Another option would be to compare image quality using an "afocal" technique. This is where a "normal" 10X eyepiece is used in the trinocular tube and a lens is used on the camera. I remember an article by Ted Clarke that outlined how he approached this... and I seem to remember that he was also using a Olympus E330. I'll check to see if I can locate it after I post this.
So your acquaintance might be troubled by any one of these things, or a combination of them.
It could also be something entirely different, but assuming things are clean and in good optical condition, and his technique is otherwise OK, these are the things I would look at.