We just had a sewer scope done as a part of the inspection to sell our house. As it turns out around 70 feet out the line drops significantly and has standing water for about 10-15 feet. I replayed the video we had done when we moved in the same conditions existed, they ran a bunch of water through it and it functioned fine and we don't ever have back ups although we did have it rooted just in case. Is this something that's somewhat normal in houses from the 1960's or does it spell trouble. My dad said it seemed like it is operating almost like a pee trap.

That's a P trap and no its not going to operate like a trap. Sags often are found in sewer drains this old. They are caused by poor installation and lack of modern techniques for sloping pipe. How large is your drain, 4"? And how deep was the standing water? A sag or belly can allow the sewage to slow down and drop some solids off which can slowly build up in the pipe. A buyer would probably never have this done during a normal inspection but that doesn't get you off the hook just yet. Now that you know you have this issue you are required to infom the buyer of a potential issue. Best bet is to get you plumber to give a written statement that he does not see this as a problem and it doesn't require repair. The plumber may not wish to do this.