A .xlsx file is roughly a zipped bundle of xml files. To unzip them, just use unzip.
Here we send the unzipped contents of myfile.xlsx to the myfile_unzipped directory, which will be created on the fly.
unzip myfile.xlsx -d myfile_unzipped
Go to the directory into which the file was unzipped.
cd myfile_unzipped
Now use find to feed all xml files to xmllint.
find -type f -name "*.xml" -exec xmllint --noout {} \;
Any xml errors will be printed out with a message like this:
./broken_example.xml:2: parser error : EndTag: '</' not found
ntType="application/vnd.openxmlformats-officedocument.extended-properties+xml"/>