The 7400 is a good deer/moose rifle. As already stated the 7400 corrected most of the deficiencies of the 740/742 early guns. I've had two, zero issues in reliability. Still have the '06, its 30 years old, I bought my .243 in 1983.
They were in big demand 30 years ago, a lot of eastern hunters wanted one. Decent accuracy, not overly heavy, and reliable and as anyone who's ever fired one down through a hardwood at a fleeing buck, they know you can't get 5 rounds squeezed of at the correct intervals with ease like you can from a 7400Remington.. I was told by a local smith who worked on many a 740/742/7400 over the years in this part of the country, a lot of problem guns had not seen any attention to the rails and port and the chambers were horribly dirty or even pitted or heavily rusted from neglect.
I just took the barrel off mine to give her a good chamber polish with drill and bronze brush. No stoppages here!
Two things to remember when using a 7400, always load your chamber from the magazine. Pull rearward fully and let her fly home to ensure complete lock up and then top up mag with four rounds if desired. You do this to ensure the rifle will fire when needed it won't if you ride the bolt home and it's slightly out of battery, or your gun is not operating as designed nad it fires while slightly out of battery and we don't want this, I never heard of it though with the 7400.
.Never put a round in a chamber first and then let the bolt fly home on it, especially on the older 740/742, a slam fire can occur. I did this many times on my first 7400, no slam fire but would never do it now, never.
And secondly,...once you've prepared your rifle for the hunt lubrication where needed for function and protection, and have secured the forearm bolt securely(I nail polish for a mild lock-tite), don't fiddle with that again till the season is over, as you can change your zero vertically tremendously if that bolt unwinds or if you tighten more without checking your zero. I find the guns will start stringing vertically on the range in hot weather with correct tension, but then again these are not 80 rounds to a range session in mid-July rifles are they, you get a free floated heavy barrel, bolt gun for this type wok,..the 7400's are one to three rounds in the fall hunting rifles and it's usually over for that session.
I tried to find a carbine length barrel for mine on the EE, but just gave up and bought a Marlin carbine for stalking work this year. I miss my BLR in Timber or hardwood when stalking.
I believe my .243Win was the second or third year the 7400's were made, so 1981 or '82 maybe the first year. If you know the serial number, just go on Remington's website and see how the serial numbers show year and month of manufacturer.