The nxt-client-0.5.3.zip.sha256.txt.asc is again a GPG signed file containing the sha256 sum. You can run "gpg --verify nxt-client-0.5.3.zip.sha256.txt.asc" to verify its content, then run "sha256sum -c nxt-client-0.5.3.zip.sha256.txt.asc" which will say "nxt-client-0.5.3.zip: OK" if the sha256 sum matches (ignore the warning about the extra lines, those are the gpg signature).
Finally, the value of the NRSversion alias on the blockchian contains the sha256 sum of the last stable release.
That gives you quite a few independent ways of verifying the package.
Add to this getting your public key based on "GPG key fingerprint" and it will be nice guide.
And yes, we definitely need nxt-client-latest to automate all this steps