Should I take my Honda to the dealership?

YEAH! He is NOT a TIMING BELT genius I would say! HE should KNOW how to do THAT type of a Job before getting you SUCKERED IN! IT is a VERY SIMPLE job for someone that does this REGULARLY! I wonder WHAT YEAR this thing is! On OLDER Honda engine the  DISTRIBUTOR is on the END of the OVERHEAD CAMSHAFT! As SUCH they are VULNERABLE to BAD OIL VAPORS that can RUIN the hall effect pickup inside them! They need to be CLEANED  every so often! And OILS that give off ACIDIC VAPORS like VALVOLINE does, should NOT be Used in them! >>HE SCREWED UP an CANNOT figure out WHERE he went WRONG! AND he has MANY Other cars w to work on and the WORK has PILED UP! NOE he is SWEATING some! YEAH I would get it OUT OF THERE! He  is STUCK an cannot figure out what to DO! CALL AROUND to OTHER shops and ASK if they have EVER done a car like YOURS before! SORRY!>>HOW OLD is this CAR! The USUAL price at a DEALERSHIP for doing a TIMING BELT WATER PUMP JOB is about $500 or so! They ALSO change the COOLANT and SHOULD do a CLEANING UP of things and a LIGHT tune up as well! You would be BETTER OF doing it YOURSELF! It is NOT hard but requires a few TOOLS and a STURDY JACK and a HAYNES manual for about $15!  They should POWER WASH the ENGIEN BAY an ask if you want NEW PLUGS in it! USE DENSO TWIN TIP IRIDIUM LASER plugs! There ae NONE better from ADVANCE AUTO! I JUST THOUGHT of something! PERHAPS he already DID bend a VALVE or TWO and now needs TIME to COVER IT UP TRY AGIAN and THREATEN with a LAWYER! I have a VERY SAD story about something like this! I TRUSTED an ARAB shop with my USED CAR GURU BENZ! They wanted a DEPOSIT and THEN kept the car for a DAMNED YEAR with NO discussion! I CRIED that I was SPENDING MONEY on INSURANCE while they DICKED around! i never saw the CAR AGAIN and they kept $1800!  they were SO dishonest that they were on HALL of SHAME! He was HIDNG CAFRS and KEEPING the DEPOSIT MONEY and telling the VICTIMS that there car was in PROGRESS!  I THOUGHT there a was SOMETHING  WRONG with this guy!  I even took PICTURES of it Sitting in the LOT ALL WINTER with NOTHING DONE! I WANTED TO KILL THEM!  I even called the local POLICE that did NOTHING!  SO I LOS ONE FULL YEAR of WORK and LOST INSURANCE over a DAMNED poorly u run SHOP! I NEEDED a LAWYER and SO DO YOU! 

The guys is an idiot and doesn't know how to reset the correct mechanical timing on the camshafts and crankshaft. 

The car is more than 20 years old.  A dealer charge to fix it would about what the car is worth.  Take it to another independent shop with a good reputation.  Or sell it and get the new owner to fix it. 

How fricken old is you car? Honda's haven't had a distributor for years. I'll bet the "mechanic" didn't get the camshaft timed to the crankshaft correctly. Better hope it didn't bend any valves!

Sounds like he does not really know what he is doing.  Hopefully he did not wreck anything.   I would say that you need to be talked through this and /or head to a dealer.