So firstly to mantis eyes, which are probably the most advanced eyes of any of my bugs, and some of the best in the invertebrate world. I touched briefly on mantis eyesight in a previous post, mentioning that they have a fovea. You can clearly see the fovea in this beautiful close-up of the P. pinnapavonis mantis, which has been named "Filthy Lucre the Sardinian Diamond Thief" or Filthy Lucre for short. A mantis' vision is its main way of detecting prey and the fovea allows it to resolve an image and actually "look at" things, rather than just detect movement in typical insect compound eyes.
The Madagascar Hissing Cockroach might not have such developed eyesight as a mantis, but it has never held them back. Cockroaches are one of the most successful organisms to have ever existed, they have been around in one form or another for 250 million years, pre-dating the dinosaurs, and will almost certainly be alive long after humans are no more. Their eyes are compound, made of many separate units called an ommatidium. All of the ommatidia together make up the outside eye which can be seen on this cockroach just above his antennae. Each one of these individual ommatidia has a nerve cell attached to the end of it that hooks up to the nervous system, and so is analogous to a single photoreceptor in a human eye, the rods and cones. In this compound eye there would be perhaps a few thousand units sensitive to light, compared with millions in a human eye, so the picture quality is nowhere near as good, but each ommatidia is very sensitive to light, so is very good at detecting movement. It is also thought that Hissing Cockroaches are also able to detect polarised light, which is used to make 3D films work. This might allow them to navigate in their natural environment but their opinion on Avatar is not yet currently known. 
The arachnids have a slightly different arrangement when it comes to eyesight, butthere is just as much variety in arachnid eyes as their can be in insects. Many arboreal, or tree-dwelling, species have great eyesight and the zebra jumping spider may have the best eyesight of any arthropod. Unfortunately for Dot the G. rosea Tarantula and Violet and Eric the two P. imperator scorpions, they are not so blessed in the sight department. Ground-dwelling species that spend much of the daylight hours underground have little use for an advanced visual system and principally use their limbs and hairs covering their bodies as their primary senses. Eyes are often described by Zoologists as "expensive" meaning it takes a lot of energy to make and run a good eye, so if a creature can get by without good eyesight then it gives it an advantage.
Still, eyes are useful things, and both Dot and the scorpions have eyes situated right on top of their head, ready to warn them if a predator such as a bird is about to attack. Spiders normally have eight eyes, and I believe that tarantulas do too, although Dot's are so small that it is hard to make out all 8 in her picture. As for scorpions, well I have no idea how many eyes P. imperator is supposed to have. There seem to be relatively few sources of information on these less optically advanced arachnids' eyes, except that the general consensus is that their sight is 'poor'. It would seem that many arachnids have both compound eyes like an insect and simple eyes made from a single lens. Incidentally, 'simple' just describes the amount of lenses, not how good the eye is - you and eye have 'simple' eyes with just one lens, but human eyesight is pretty good. From a couple of googles the main priority we have with tarantulas and eyes, even in academic work, is with the potential damage that their urticating hairs can do to human eyes. There is very little work that appears to have been done on how well many arachnids can actually see. Maybe it would be better if we all feared these amazing guys a little less and wondered about them a little more.
