Cows are prone to respiratory issues as they have very small lungs (the size of humans) for how big they are. I’ve had calves arrive with pneumonia which can be the result of stress, poor hygiene and traveling in bad weather. It cleared up with Draxxin which is an antibiotic.
Lice and mites will become a normal yearly thing you’ll need to prevent and/or treat with products like ivomec, cydectin, pyrethrum powder, or clean up ll. There are also internal dewormers such as Safeguard you may want to consider. Everyone uses different products and rotating them can be beneficial by avoiding resistance to any single product. Don't worry, the lice and mites that cows get are not contagious to humans or other animals.
Juvenile warts are common growths on cows under 1 yr old. If they are small you can leave them alone. If they get bigger, like grape size, you can remove them or treat them with wart off. If they get near their eyes, have your Vet check it out. They are contagious to other cows but very common and nothing to panic about. They will go away on their own within 4-6 months usually and they are generally immune to them after that.
Ringworm is another cow ailment, however this one is contagious to you and other animals. It's easy to identify as it looks like well-bordered bald patches. You're most likely to see this occur in the spring and temperatures warm and rainfall and humidity increase. Brushing away loose hair and mats, and providing dry bedding and shelter is the best preventative. You can treat active patches by applying iodine or aloe vera gel to the bald spot for a few days. Wear gloves, and disinfect combs so that you don’t spread it. Sunshine will also kill it. Despite it's name, it’s actually a form of fungus.
Pink eye is something to watch carefully for during fly season. If you have a good fly prevention program, you're less likely to run into it. I keep a bottle of vetricyn pink eye spray around and teach my calves when they're young to trade me treats for eye spray. It’s surprising well received. Anytime their eyes look irritated or crusty, I simply clean them with the spray to avoid them becoming infected.
Scours (diarrhea) is also something to be mindful of with calves. Full blown scours (liquid poop, blood) is something you’ll likely want your Vet out to help you with. You’ll need isolation / meds / fluids, etc. Sloppy poops can be coccidiosis or the result of stress and diet change, dirty water, etc. In these cases if it continues for more than a few days, treating for coccidia with Corid is a good idea. I keep a product of First Arrival around for this too and it helps a lot with travel stress and diet change.
So much can be prevented by keeping their areas and water clean, consistent diet of quality hay and minerals, brushing regularly and vaccinating annually… at least the core vaccines but check with your Vet to see if there’s anything in your area that you should also include.