Rewards for those who aren't actually bothering to work
I wouldn't file this one under "signs that your company is losing its way", but it definitely goes in the "fail" bucket.
Let's say your company has some kind of internal giveaway going on. They use some technical method to let people sign up for things in a first come, first served order. Whoever gets to the web page and does the necessary registration stuff gets put in a queue and gets a ticket. That ticket is later redeemable for the actual prize, like a DVD.
Then, when the DVDs come in, someone just says "if you want one come and get one". Not surprisingly, all of the copies disappear into the hands of people who work close by and were polling their mail instead of actually working. Anyone who was relatively distant, at lunch, in "heads-down hack mode", or anything else of the sort lost. They effectively rewarded the people who had nothing better to do.
It's one thing to do this sort of giveaway from the outset and mess it up, but when you've already given out tickets, it makes no sense. There's a good chance that whoever handled it had no way to realize what the bigger picture looked like and why that was a bad idea.
Not seeing the forest for the trees? Sure, why not.