Calling the grievance process a deplorable joke is a compiment. If your company takes disciplinary action against you, the grievance process could get your job back for you. The problems with it are:
1) It could take years
2) The only one that suffers will be you
3) There is no punitive action against the company so they will continue with whatever behavior warranted the grievance
4) Your union will probably negotiate your settlement away in exchange for the company's promise that they'll never do "that" again
5) Reading in the magazine that the union scored a huge victory for the pilot group after they got you .036% of what was owed to you, which was written by someone who earns their salary from your union dues, was slightly offensive.
The current system just doesn't work. If you have the funds to be unemployed for years, fight it with the union. If you actually want to see results, I'd probably hire an attorney.
I'm not bagging on union guys. Some of them work very hard. The problem is the system. We're throwing stones at the nuke plant because the rules says we have to.