Yes slimy broccoli is bad and should not be eaten especially if the broccoli is really slimy.
If the broccoli is slimy and or has started changing colors then the broccoli should be thrown out because it has gone bad.
When broccoli goes bad the broccoli will begin changing colors and the bright green color of the broccoli begins to turn yellow and it's crisp texture will become limp.
That is a sign that broccoli has gone bad or is going bad and should not be eaten.
When broccoli is fresh it should be a bright green color and not be limp or shriveled and it should not smell bad.
If the broccoli smells bad, is slimy or has changed color or has any mold growth on it then throw the broccoli out because it has gone bad.