B737-300 FO ON SHORT FINAL TO RWY 24R AT CLE NEARLY MAKES LOW LEVEL GAR DUE TO ACFT CROSSING RWY THRESHOLD. TRAFFIC CLEARS JUST IN TIME TO COMPLETE LNDG.

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WE WERE ON A VISUAL APCH TO RWY 24R IN CLE; AND IT WAS NEARING XA00. I WAS FLYING; WE WERE CLRED TO LAND; AND WE WERE ON SHORT FINAL. APCHING AN ALT THAT I ESTIMATE TO BE BTWN 200-100 FT; I SAW ACFT LIGHTS ON THE GND SLOWLY START TO TAXI ACROSS THE THRESHOLD OF OUR RWY. THE CAPT QUERIED THE TWR TO CONFIRM THAT WE WERE CLRED TO LAND; TO BRING IT TO THEIR ATTN THAT WE WERE ON SHORT FINAL; AND THAT THERE WAS AN ACFT ON THE THRESHOLD OF OUR RWY. WE WERE NOT TOLD OF AN ACFT THAT WOULD BE XING OUR RWY BEFORE LNDG. I WAS CONCERNED THAT THE ACFT WAS NOT GOING TO BE ABLE TO CLR THE RWY BEFORE WE LANDED. I WAS PREPARING TO GO AROUND; AND THE ACFT CLRED THE RWY WHEN WE WERE AT A VERY LOW ALT; BUT BEFORE THE 50 FT CALL. I LANDED THE ACFT AND WE TAXIED IN NORMALLY. I THINK THE SEPARATION OF OUR ACFT AND THE ACFT ON THE GND WAS REACHING AN UNSAFE CLOSE DISTANCE. I ASKED THE GND CTLR FOR THE PHONE NUMBER OF THE TWR; AND I CALLED THE TWR AFTER WE WERE AT THE GATE AND FINISHED WITH ALL OF OUR CHKLISTS. ONCE I WAS ABLE TO REACH THE SUPVR IN CHARGE; HE WAS VERY RESPONSIVE ON THE CALL; AND I THINK WE HAD A PRODUCTIVE TALK OF THE OCCURRENCE. HE SAID THAT HE WOULD TALK TO THE CTLR THE NEXT DAY; AND HE APPRECIATED MY CONCERN. ON ANOTHER NOTE; HE INITIALLY THOUGHT I WAS 'THE AIRPLANE THAT WENT AROUND BECAUSE OF THE DASH ON THE RWY' NEAR THE SAME TIME THAT MY OCCURRENCE HAPPENED. MAYBE THIS IS A PROB AT THIS ARPT; OR MAYBE THESE ARE ISOLATED INCIDENCES.