Whenever your cat starts acting differently, weird in any way, you need to identify the cause and see if any intervention is needed from your side to fix it. This may not be easy - cats have, by nature, the tendency to take care of themselves and to resent any outside intervention unless requested. However, they might appreciate the help once it is given.
When you smell cat problems, the first step is to identify exactly what is going on. Every small deviation from usual behavior may be a sign of a health issue, so don't dismiss it until you are completely sure that nothing is going on. Especially in the case of older cats, health issues can occur quite frequently. Definitely take the cat to a doctor if it starts losing weight, stops eating and starts spending much more time sleeping than usual.
Cats occasionally experience behavioral problems if they have recently changed owners - despite common opinion that they do not get attached. Such cat problems usually have visible signs like scratching and fighting and you may need to spend some time getting your cat to know you and trust you. If there are other cats in the house, the new cat may also have a tendency to spray and mark its territory - try to show it that this is not OK, so that, in time, it drops the habit.
Cats usually take care of their own hygiene, but grooming problems may appear. If their hair starts falling, hairballs might form and, by swallowing them, the cat may start having digestive issues. You may want to take it to the vet for both these issues: the excessive hair loss and the stomach issues.
Cat problems - how do you approach them?
One of the most common personality traits for cats is independence. For that reason, the owners must find middle ground between indifference (which may occasionally seem to be what the cat wants) and suffocation (which will send your cat running up the hills). You need to cleverly watch your cat without giving it the impression that you are spying on it. Learn its behavioral patterns and learn to spot deviations.
If you don't want your house full of kittens, you may want to make sure your cat is neutered. A cat pregnancy in itself can cause lots of issues, destabilize the patterns for two months and, of course, fill your house with way more cats then you can handle.
Also, make sure that, even if nothing is happening that seems out of the ordinary, you take your cat to the vet frequently - some issues develop over time and it is always much better to prevent than to heal. Cat problems can be easily foreseen and prevented with a little bit of care and affection.