1. Vinegar (and lemon, and "natural" cleaners)
Vinegar is acid. Travertine and marble are calcium carbonate, and acid dissolves them. Vinegar leaves dull, etched patches, especially if you use it often. "Natural" citrus cleaners do the same thing.
Do this instead: pH-neutral stone cleaner.
2. Bathroom and lime-scale sprays
They're designed to dissolve mineral scale, and your stone is mineral. Read the label. If it says "not for marble or natural stone," take it seriously. More on this in hard water and stone.
3. Mop-and-shine products
They leave a film that looks shiny at first, then builds up, traps dirt and turns cloudy. Getting it off later is a job. It's one of the most common things I strip off travertine before I can work on the stone.
4. Steam mops on every floor
Heat and moisture can be hard on sealers and fillers, and some manufacturers say not to use steam on natural stone. Check your sealer's guidance before you steam.
5. Hardware store "shiny" sealers on stone
A topical acrylic coating looks great for a month. Then it scratches, yellows and peels, especially outdoors in our sun. Travertine usually wants a penetrating sealer that soaks in. See cleaning & sealing.
6. Sealing over dirt
If you seal a dirty floor or dirty grout, you've locked the dirt in. Clean thoroughly and let it dry first.
7. Scrubbing with abrasives
Green scrub pads, powdered cleansers and wire brushes scratch stone, especially polished stone. Use soft pads and let the cleaner do the work.
If you already did one of these
Don't panic. Most of it is fixable. Etching comes out with honing, and coatings can be stripped. Send a photo to (702) 400-0360 and I'll tell you what I think.