MLG HAS OVER SPD WITH FLAP EXTENDED 1 DEG. NOTE ABNORMAL AILERON DEFLECTION TO R.

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DEPARTED RSW ENRTE TO DFW WITH NUMEROUS TSTMS; RAINSHOWERS IN THE AREA. FELT HAD PLANNED WELL; CONSIDERED MANY SOLUTIONS TO GETTING FLT AIRBORNE AND SAFELY UNDERWAY. CAPT (SELF) AND PNF HAD BRIEFED WITH FO; PF; ON SPECIFIC DUTIES; TASK; AND RESPONSIBILITIES FOR THE DEP. AFTER TKOF; FO (PF) MADE NORMAL CALLS; EXCEPT FOR 'FLAPS UP.' FLAPS HAD ALREADY BEEN RAISED FROM 5 DEGS TO 1 DEG DURING DEP. BELIEVE FO DELAYED RAISING FLAPS TO '0' DEGS IN ORDER TO IMPROVE MANEUVERABILITY AS WE DEPARTED. SEVERAL QUICK AND TIMELY TURNS WERE REQUIRED TO AVOID SIGNIFICANT RAINSHOWERS. BECAUSE OF WX; DEP PROCS WERE OUT OF SEQUENCE OR DELAYED. FO DID CALL FOR 'AFTER TKOF CHKLIST;' BUT I DELAYED COMPLETION IN ORDER TO MANAGE RADAR AND PLAN RTE TO MINIMIZE ROUGH RIDE AND HVY RAIN. DUE TO TASK SATURATION; WE OVERSPED THE FLAP'S 1 DEG POS BY APPROX 11-14 KTS. ACCELERATED TO 245 KTS (APPROX) WHEN REALIZED HAD NOT RAISED FLAPS TO UP (LIMIT 230 KTS). FLAPS WERE RAISED AND ALL FLT DECK INDICATIONS WERE NORMAL. APPROX 20 MINS LATER; WHEN ACCELERATING TO 310 KTS (DELAYED ACCELERATION DUE TO ROUGH AIR); NOTED ABNORMAL AILERON DEFLECTION TO R. LOOKED OUT WINDOW AND SAW #2 (ON L WING) SLAT STILL PARTIALLY EXTENDED. SLOWED ACFT AND DSNDED TO FL200. COMPLETED CHKLIST AND DECIDED TO DIVERT TO ATL. EMER WAS DECLARED. CONSIDERED SELF TASK SATURATED DUE TO WX AVOIDANCE; POOR DECISION IN DELAYING 'AFTER TKOF CHKLIST.'