I've solved this myself, but in case anyone else has this problem: I was trying to import an Excel worksheet as an Access table. Several of the worksheet columns were formatted as dates, but the import failed because of many type conversion errors in two of the date columns. I tried changing the date formats in Excel, but none of my changes seem to fix the problem. I exported the entire Excel file as a tab-delimited text file and imported that into Access, specifying Date/Time format for each of the date fields, but the same errors occurred.
I finally opened the Access table in Design view and check the formats of the fields I wanted to be dates. Their Data Type was Date/Time all right, but under Field Properties I hadn't specified anything for Format. I specified Short Date (6/19/2007), which is what I wanted anyway, and tried the import again. This time the import was successful, with no errors.
Oddly, when I rechecked the date field's formats in Access after the import, I found they had reverted to blanks in the Field Properties' Format field. Oh, well. . .