The OEM transmission mount collapses, which can actually occur with the passage of time as well as accumulated mileage. And guess what, one of the symptoms is problematic shifting. There aftermarket replacements as well as a less expensive-easier to install "insert" to "un-collapse" it.
The motor mounts are liquid-filled units which eventually develop leaks. The leakage leaves telltale signs of brownish liquid in the vicinity of the mounts. The motor mount failure rate varies more with how many times the driver "punches" the throttle.