How to extract and join files xxx.zip, xxx.z01 and xxx.z02

Try:

zip -FF 1.zip --out 1-full.zip
unzip -FF 1-full.zip

I think most likely some data is broken many times so you need the -FF still in unzip. A single -F may work also though.

I have the same issue today with Mass Effect 3. Someone broke the installation of Mass Effect 3 in new version of origin on windows and my wine of course too (installation hangs on 99%). I have to make manually installation:

cp /mnt/cdrom1/Mass\ Effect\ 3.z01 ~/temp/Mass\ Effect\ 3.z01
cp /mnt/cdrom2/Mass\ Effect\ 3.zip ~/temp/Mass\ Effect\ 3.zip
zip -FF Mass\ Effect\ 3.zip --out Mass\ Effect\ 3.zip.fixed
mkdir Mass\ Effect\ 3
unzip -d Mass\ Effect\ 3/ Mass\ Effect\ 3.zip.fixed
du --total Mass\ Effect\ 3
>> 10466048 (~10.5 GB => success)

zip -FF should be applied to last part of archive, it will automatically check for all parts

Put all your zip files in the same directory: zip_file.z01, zip_file.z02, zip_file.z03, ..., zip_file.zip

In Zip 3.0 version the following commands worked for me:

$ zip -s- zip_file.zip -O zip_file_full.zip
$ unzip zip_file_full.zip

As noted in the comments, using a - sign after the command line option -s joins all the zip files together and writes it as a single zip file which you can then extract using the unzip command.