A CLBING B737-300 OVERSHOT ITS ASSIGNED ALT OF 5000 FT BY 1000 FT. FO WAS IN TRAINING.

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I LEVELED OUT AT 6000 FT INSTEAD OF 5000 FT AS ASSIGNED IN ATC CLRNC. I HONESTLY DON'T KNOW IF I MISREAD THE ACARS CLRNC AND MISDIALED THE INITIAL ALT OR IF I WAS DISTR WHILE SETTING UP AND 6000 FT WAS LEFT FROM PRIOR LEG. AT ANY RATE; 6000 FT WAS MISTAKENLY SET AND NOT CHALLENGED LATER. THIS WAS AN IOE TRIP AFTER FINISHING TRAINING. I MAY HAVE BEEN TOO FOCUSED ON PROPER PROGRAMMING OF FMC AND NOT ENOUGH ON BASICS. ALSO; A SHORT TAXI/HIGH WORKLOAD TAXI OUT HELPED TO KEEP US FROM CATCHING A BASIC ERROR. LONG AND SHORT IS -- ALL BASIC CLRNC INFO MUST BE DOUBLECHKED AND CONFIRMED EVERY TIME. SUPPLEMENTAL INFO FROM ACN 411744: DURING CLBOUT THE STUDENT; FO IN TRAINING; SET 6000 FT IN THE ALT WINDOW. THE STUDENT HAD BEEN ON A SIMILAR FMC ACFT THAT HAD EFIS. ON CLBOUT FROM DCA; WHILE LEVEL AT 6000 FT; THE CTLR ASKED ABOUT OUR ASSIGNED ALT. DUE TO PREVIOUS INCORRECT LATERAL NAV ENTRIES; COCKPIT ATTN WAS DIVERTED FROM ALT READINGS/CHKS NORMALLY ACCOMPLISHED. BUSY; SHORT TAXI PATH INVOLVING HIGH WORKLOAD DURING BRIEFING. RADIO CONFUSION ABOUT XING RWY 33. GLARE ON ALT WINDOW LCD READOUT; MAKING IT DIFFICULT TO READ. SHORT TAXI RTE; TEACHING ENVIRONMENT DURING HIGH WORKLOAD. TWR RUSHING OUR ACFT TO FILL AN 'ARR SLOT' FOR OUR DEP RESULTING IN CHKLISTS BEING ACCOMPLISHED QUICKLY. ACARS DEP INFO BEING LOCATED WELL BEHIND THE PLT'S NORMAL FIELD OF VISION AND REQUIRING INFO TO BE READ SIDEWAYS. STUDENT'S INCORRECT ENTRY (LATER CORRECTED) IN THE LATERAL DATA NAV BASE REQUIRING SEVERAL CORRECTIVE ENTRIES BY BOTH PLT AND DIVERTING ATTN DURING CLBOUT. RECOMMENDATIONS: STUDY FEASIBILITY OF ACARS DATA BEING PLACED/REPEATED TO PLT'S NORMAL FIELD OF VISION.