What do you mean by safe? Is the server as secure as your online banking? Probably not! Will anyone steal your data? Very unlikely!

Molprobity is the current validation suite of choice, and the one used by the PDB in its validation suite. You can upload files to the PDB server at http://wwpdb.org/validation-servers.html to see how the PDB will validate your structure.

I don't see why it would not be safe to use the online server. Only you have access to the results.

In our lab we use the PSVS web server, which give a more complete set of statistics (it also uses Procheck for the geometry): http://psvs-1_5-dev.nesg.org/

It is safe to use Procheck online server. However, I will recommend you try to use Molprobity for a complete analysis of protein structure. 

Hi, You can use PDBSUM web interface (http://www.ebi.ac.uk/pdbsum/) for Protein structure quality analysis. For your own PDB file, you have to go to "Generate" option in PDBSUM webpage.

You can also use SAVes server from NIH ( http://nihserver.mbi.ucla.edu/SAVES/ ). I think you are using the same NIH server for Procheck also. But if you use the SAVes server, then it will give you the full analysis of your structure as it includes different sub-servers. It is completely safe.

Another good and safe resource to check your geometry is MOLPROBITY:

http://molprobity.biochem.duke.edu/

Absolutely safe. Your submitted data gets cleared off the server automatically.