About your background noise problem: No one else has reported it. My 690 has a VERY weak hiss that's barely audible, and it's present in any mode (tuner, CD, tape, or external), but it has nothing to do with the modification. Check all of your work for cold solder joints. A bad solder joint can act as a diode/detector that could potentially pick up local Radio,TV, or Ham stations and introduce that sound into your boom box's amplifier. Failing that, try putting a ~.001UF capacitor from ground to input connection for both the left and right channels. This will usually block external transmitters from getting into your amplifier section.
The aux input modification has no effect on tape speed. Either the unit had that problem before you did the mod, or you made some kind of wiring mistake. Check the 2nd tape's drive belt(s) too- its possible that one of them came out of its pulley groove and it's riding on the pulley's hub. This could cause speedup.
Thanks to alltare and others for this very handy mod. I recently bought this radio to take out to parks, the beach etc but was disappointed to find it doesn't have an aux input from factory (who uses tapes and cd's these days? haha).I performed the mod, took a little longer than I expected after a couple of hiccups but now I have a 3.5mm closed circuit jack flush mounted on the rear of the unit.
The only minor problem is I have a quiet background noise when I have a source plugged into the newly installed input on the back. You can only hear it when there is no music and the volume is at moderate levels. I can't pinpoint where the noise is coming from, it only happens when you plug something in. When nothing is plugged in the circuit from the tape deck works as it should with no interference... if you plug in a 3.5mm cable into the stereo it is fine, but when you plug the other end of the cable into something else that's when you get the mild interference. It's not a big deal, as it's only quiet... and really it's not a piece of audiophile equipment it's a portable stereo, but if I know whats causing the noise I might try and fix it. There is no noise when playing cassettes, so I can assume it's grounded OK?
Overall I'm very happy with the mod, the quiet noise is not overly bad and is a small trade off to have an aux input on the unit. One other thing though, I'm not sure if anybody would know... My second tape deck appears to be stuck on high speed mode, weather or not your playing, recording or dubbing... It just runs too fast. The first deck is fine. Could I have possibly knocked a switch or something to cause this? I couldn't find anything after having a look... I don't know if I caused this or not as I didn't test out the tape decks before I installed the line in.