In general, Opuntia's are sturdy plants, and far more forgiving than Sclerocacti or Phyrrhocacti. But they can get pests. I used to have mealy bugs on my plants, but in recent years they have not been a problem. I attribute this to the high temperatures in the greenhouse. Root mealies might be there, but in general root mealies are far less a problem on mineral soil than on peat based soils. Spider mite are not really a problem. There might be some aphids on buds and young pads, but they won't last long, as fully grown pads are to tough for them.
What does happen are fungus. They might not kill your plants in the greenhouse, but they might become unsightly. Try to not give your plants too much water, and aerate as much as you can. Stagnate air is not good. I keep my vents open all the time, unless it's raining or during cold weather (and thats's much more because of other, marginal plants). The minimum opening of my vents is 10 cm.
In the garden snails and slugs can be a real problem. New pads can be devastated overnight. A constant look out is needed.