Yes, mould (or mold) can be invisible. When an item is visibly moldy, the visible part of the mold is actually the fruiting body. (You can think of a "fruiting body" like the flower on a plant. It's the structure that produces and distributes spores, much like flowers produce seeds.) The main body of the mold is a fine network of root-like structures called hyphae. The hyphae extend through the food item, digesting it to convert it into food for the mold. Once the mold has enough energy, it produces fruiting bodies, which in turn produce spores that allow the mold to spread through the air to other food items.
Hyphae are usually invisible to the naked eye. So yes, you could be eating food items that have mold hyphae growing through them that just haven't fruited yet. The hyphae cause chemical changes in the food which make it unsafe to eat.
I've noticed this myself with homemade baked goods that have sat around for several days. There's usually a period of a day or two where the item will taste strange, but before there's visible mold. (Interestingly, the particular strain of mold I have in my kitchen tastes a bit like cooked pineapple. I love pineapple, so it actually tastes good at first.) I often eat half a muffin or slice of bread before noticing that it has an unusual taste. But partway through eating that muffin, I'll start to notice the new flavor, and it starts to taste not so good.
My advice is to listen to your taste buds, and if you get partway through eating something and it starts to taste bad to you, take that as a sign that it might not be a good idea to continue eating it. That feeling is not always because of food spoilage, though. Sometimes it's because you're starting to get full, or the food is too salty, or one of a long list of other reasons why that food item might not agree with you.
Try to pay attention to what food items start to taste bad to you, and look for patterns over time. If it's usually with a particular type of food that's been sitting around for a while, then maybe you're not storing that food correctly and it's starting to spoil. If it happens repeatedly with different batches of the same type of food, you may have an allergy or sensitivity to an ingredient in that food, and you should consult a doctor or nutritionist for help in figuring that out. Some foods, like apples and potatoes, have a high satiety value. Foods with a high satiety value can make you feel like you've had enough to eat before you've actually eaten enough, and continuing to eat that food may make you feel nauseous. This is useful if you're trying to lose weight, but inconvenient if you have a small budget and you're trying to make that food item a staple of your diet.