This is certainly an issue that is occurring more often in the field. While standards bodies suggest not mixing media in a network, there are certainly cases where it is necessary, for example, when a company is migrating to new technologies or, as in the case of your client, where they are cabling an additional building. There are two ways this can be accomplished: either through an optical connection or through network electronics.
The more straightforward approach is to make the connection between the two media types through the electronics and not in the patch panel. In this scenario, if you are bringing in a 50 micron cable to connect the two buildings there are no issues as long as the 50 micron cable comes into a patch panel and you use 50 micron patch cords to connect straight into the equipment (rather than connecting the 50 micron and 62.5 micron in a patch panel). Bringing the 50 micron cable into the legacy equipment makes good sense and prevents the customer from having potential power budget issues. The launch loss from the electronics into the 50 micron will be higher, but that loss is offset with higher bandwidth, in most cases, so the system works fine. The only other issue is to make sure you have some way of identifying the 50 micron from the 62.5 micron, either through labeling or color coding.
Optical connections are trickier. Although it is technically feasible to combine 50 micron and 62.5 micron core multimode fibers in the same system, there is a one-time attenuation loss when coupling 62.5 micron fiber into 50 micron fiber. This one-time power loss is independent of the number of connectors and fiber type changes that occur in a cable run. Testing by FOLS member companies have shown that this loss is small when there is good coupling alignment and when lasers are used as the transmission source (instead of LEDs). Excess margin in the fiber (or in the transceivers) can, in some instances be used to overcome the extra coupling loss. The optimum solution for a particular system will depend on the system requirements (speed and link length) as well as the type of transceivers used.