Watch erratic. Slows suddenly between days of working well.

Lots of older watches needed to have the hands advanced 24 hours to advance the date one day. Fortunately most modern watches require the hands to be wound backwards to advance the date, often at the rate of a day per hour. A combination of the backward and forward winding of the hands made adjusting the day and date much simpler and quicker.

A few premium watches had a third position when pulling out the winder, a position dedicated to adjusting the day/date

So answering this many years after you posted. But I just found my sane watch in a drawer and decided to tinker with it. The watch is only part automatic. That works the second hand. The hour and minute hand runs on a battery. It's inside and under the auto part. One screw and you work see it. Easy fix.

Adjust the day of month (1-31) by pulling the crown pin out part way, and turning the pin counter clockwise, incrementing the date arm. Counterclockwise does nothing.

To adjust day of week (Mon-Sun), pull the pin out and rotate to turn minute/hour hands. Each time you pass 12:00, the weekday hand will increment by a half step.

There are two crown positions on this timepiece. The furthest out, or second position, sets the analog time hands. The first crown position in one direction sets the day, and in the other sets the date. To access the first crown position, pull the crown out very slowly until you feel a "click" or pull the crown out all the way and push it in slowly until you feel a "click" with your fingers.

To set the watch:

1) Pull the crown to the second position and bring the hour and minute hand to the 12:00 position, if it switches the day and date after moving past, you are then in AM time.

2) Set the time appropriately to AM/PM. Use http://www.time.gov/ for the most accurate time.

3) Put the crown in the first click position. Set the Date and Day appropriately, having determined the AM/PM time setting. This will ensure that the day/date change at 12:00 midnight instead of 12:00 noon.

Sorry to say it's a reproduciton..and not a very accurate one..

The three front dials should not reference any days hour dates etc..

There should be nothing engraved on the back

The "second hand" is a sweep timer hand on the original.. it should be stationary at the noon position unless activated.

Probably a good looking watch.. but it's not a Rolex.

Best of luck

Your watch's hour hand is a bit loose or hour wheel skipped a few teeth and now is not in correct engagement. To solve this you need to visit your nearest watch repair shop and ask for help as you don't have knowledge and specific tools to carry out repairs. Any attempts to solve this without special tools and knowledge will definetely damage your watch.

Rate, please.

If new, just take back and exchange it for another working one.

The advice given here is accurate to a degree. When wound, a rolex daytona IS running. However, it is the running seconds hand in the small sub-dial that is actually running. In the earlier Daytonas, this sub-dial was at the 9 o'clock position on the dial, (pre-2001 series daytonas). The later daytonas, from 2001 on, use the seconds at 6 position for counting seconds. The main sweeping second hand on the watch dial will NOT start until activated by the pusher at the 2 position. That pusher needs to be unscrewed and then pushed to start the large sweeping second hand. This action, in turn, starts the remaining 2 sub-dials in motion, counting minutes and hours. To stop the chronograph function, you push the pusher @ the 2 position again, to stop the sub-dial hands from counting, and then push the pusher @ the 4 position to re-set the dials to their "straight up position". This stops the chrono's function, until it is needed again, BUT the main running seconds, (at either the 9 or 6 sub-dial position, depending on the year series of the daytona) will continue to run, thus keeping accurate time.  Hope this gives you a better idea of how the timekeeping of the chronograph function on a Daytona works. So, to start your seconds running you need to start the chrono function by pressing the pusher at the 2 position. That will allow you to see the large sweeping second hand I think you're referring to here. Hope this has helped.
Doug