IN AN ATTEMPT TO EXPEDITE TFC; LCL CTLR AT SJC ALLOWED AN ACR TO MAKE AN INTXN DEP WITH ANOTHER ACR IN POS AND AN ACR ON SHORT FINAL.

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GND CTL HAD AN LAX DEP WITH A FLOW TIME OF 12 MINS AFTER THE HR; ACR X. GND CTL WANTED TO COORDINATE A RWY XING AT TXWY C TO GET HIM #1 TO THE RWY TO MEET THE FLOW VIA TXWY C AND TXWY W. AT THE TIME; THE LCL CTLR PUT A DC10 IN POS AND HOLD; ACR Y. THE NEXT ARR WAS 6 MI FINAL APPROX 170 KTS GND SPD; ACR Z. THERE WERE NO OTHER ARRS AT THIS TIME. I TOLD GND CTL TO BRING ACR X TO INTXN C FOR DEP; THAT WE COULD GET HIM OUT FROM THERE. MY PLAN WAS TO DEPART ACR Y AND BY THE TIME ACR Z LANDED AND EXITED THE RWY; WE WOULD HAVE 3 MINS FOR WAKE TURB AND MEET THE LAX FLOW TIME. I CALLED SARATOGA SECTOR AT BAY TRACON FOR A RELEASE ON THE ACR X FLT. AS ACR X WAS MAKING THE TURN ON TXWY C; LCL CTL CLRED ACR X FOR TKOF. I WAS COMPLETELY SURPRISED BY THIS BECAUSE THE DC10 WAS STILL IN POS AND THE ARR WAS COMING INSIDE 5 MI FINAL. THE OTHER CONCERN WAS THAT ACR X AND ACR Y WERE ON THE SAME SID AND WE ARE REQUIRED TO GIVE BAY 7 MI INCREASING TO 10 MI WITH THIS SET-UP. I REMINDED LCL CTL THAT HE HAD TFC IN POS. HE THEN INSTRUCTED ACR X TO DEPART WITHOUT DELAY; EXCEPT HE CALLED HIM ACR XX. ACR X ACKNOWLEDGED. BY THE TIME ACR X BEGAN DEP ROLL; THE ARR WAS ON 2 MI FINAL. LCL CTLR TOLD ME TO COORDINATE AN EARLY R TURN WITH BAY TRACON; WHICH I DID; AND RECEIVED. WHEN ACR X BECAME AIRBORNE; THE ARR WAS ON 1 MI FINAL 400 FT. LCL CTLR ISSUED A GAR TO ACR Z FROM DIRECT MAINTAIN 3000 FT. MY NEXT CONCERN WAS THAT ON THIS GAR HDG WE DID NOT HAVE 2 MI INCREASING TO 3 MI. ALSO; HE MADE NO ATTEMPT TO GET VISUAL. I CALLED BAY AND ADVISED WE HAD A GAR. HE ASKED IF THE DEP WAS AIRBORNE. I SAID 'YES; WOULD YOU LIKE ACR Z ON A 270 DEG HDG?' HE SAID 'NO; TURN THE DEP.' I TOLD LCL TO TURN ACR X TO R HDG 120 DEGS VECTORS TO AVE. LCL SAID HE ISSUED A FREQ CHANGE. I DIDN'T HEAR IT; SO I ASKED HIM TO CHK. THIS WAS NOT DONE. 5 MI UPWIND; ACR X ASKED FOR A FREQ CHANGE. I TOLD LCL CTLR TO TURN HIM R HDG 120 DEGS. LCL CTLR ISSUED FREQ CHANGE. HE THEN INSTRUCTED ACR Z TO TURN R 120 DEGS. I CALLED BAY TRACON 'BREAK FOR CTL' AND ADVISED HIM THAT THE GAR WAS ISSUED R TO 120 DEGS. BAY TRACON SAID 'CLB TO 4000 FT.' I SAID 'WILCO' AND TOLD LCL CTL. LCL CTLR ISSUED 4000 FT TO ACR Z AND FREQ CHANGED. IN THE CLBING TURN; THE CONFLICT ALERT WARNING WENT OFF BTWN ACR Z AND A PA28 N OF THE FIELD. I DID NOT NOTICE THE PROX OF THE PA28 UNTIL THE WARNING WENT OFF.