I have an access database that was created in a 32bit version of windows, can there be any problem using it in a 64bit version of MS Access?
If your database is a .mdb or .accdb file you should have no problems. A compiled .mde, .ade or .accde database is not portable between the 32 and 64 bitness as described in this forum and technet article.
You will see the error message The database was created with the 32-bit version of Access (duh). Please open it with the 32-bit version of Microsoft Access