That second arm movement you describe is kind of "normal" with SL10s, as mine will do the same thing: the needle touches the lead-in groove and as soon as the sensor calculates how far the arm has already travelled before the automatic lever releases it, it quickly sets itself into position. Maybe there's a bit of hardened grease in the rod that the arm slips along, holding back the arm a little, stalling the movement. In an attempt to soften the abruptness, I recently interrupted playback with the stylus halfway through the record and opened the lid, so the arm stayed in position. I was then able to clean the little bit of hardened grease that was in the arm's initial position in the rod with a "pamper's" type towel. As for the other symptom, if I get it right (the arm moves too far in the direction of the record stamp), that can be fixed be repositioning the "stop-screw sensor" that the arm touches when it reaches the end of the record. The instructions in the manual imply breaking the black plastic strip that hides the screws that hold the perspex on the lid. That's ridiculous. I accessed it by removing the black cowling that covers the mechanism, in the inner side of the lid, instead. An adjustment is possible for records with smaller stamps, or for certain albums contaning a last track that is too long. Mine, for instance, will not play "Sometime Salvation" on the Black Crowes album fully. I mean, the arm touches the sensor screw before the end of the song, no matter how I reposition the sensor.
Hope this helps.