About the batteries suggestion: no, not the 4T (or 4Ti) - the batteries are an issue in the plain OM 4, which has had three or four revisions of its circuitry. When the problem was solved, the 4T(i) was launched. Anyway, check the batteries as this rules for any electronic camera and be sure they put out 1.55V. The Energizer are recommended by some knowledgeable users (check the Olympus mailing list archives, search Tim Hughes' posts), but I've used the Swiss-made Renata with no problems. I own both the 4 and the 4Ti, and batteries are an issue in the 4 only.
The jammed shutter is a known issue of both 4 and 4Ti, not so in the 2n or plain 2, 1n or plain 1. Don't know about the 2s or 2sp, and never heard a 3Ti or plain 3 suffering this.
And yes, John Hermanson can fix it.