That magnifier will come in handy with just about any exam whether it's on a deck you own or thinking about buying. I keep meaning to buy one with a light on it. Using a light and magnifier is maddening. Take a 10.5" reel of familiar material with you. Something like solo piano is good. You want to listen to just 5 minutes or so to see if you can hear any audible flutter. Take enough time to ff/rewind and stop the deck at least once at the beginning, middle and end of the tape. This will test the braking and reel motors on both reel tables. When the weight distribution is as far from even it makes starting and stopping the most difficult. After the stops, hit play and stop a couple of times too. There's several things that happen at the same time when you hit play or stop from play. These things need to happen harmoniously (timing wise) or things like tape slack or the audible sound of the tape getting up to speed can be heard in playback. Bring a blank tape with you. Hook up the deck to anything and even if you don't, do a test recording. If the deck has a headphone output, listen while you turn the line/mic level up and down and then the output level level too. Switch every control in and out. Even if you have no plans to use a control, it's improper behavior might indicate a deeper problem or at least represent a bargaining chip on the selling price. One of the last things to try are the speed adjustments. If there's a problem with the motors or servo on the motors, the warmer they get, the more prone they seem to be to fail. Don't ask me why, but maybe someone that knows how these things work can chime in. One last thing, try and keep a tape treaded on the machine as much of the time your there as you can. Unless the tensioners are engaged, the capstan motor won't run( you want to give it a chance to fail too) and after you take your tape off the deck, test the tensioners with your finger, it should turn on the capstan quickly.
During all these procedures, keep an eye on how evenly the tape is being wrapped. On play, the outside of the tape should be smooth and even. Uneven tape wrap can indicate lots of tape handling or tape problems.