The other answers already mentioned polycoria. However, unlike Cognisant's answer, this is a known and well documented malformation of the eye in humans. You can google that word and look for images to see it for yourself.
The wikipedia article for it is very lacking, so I went looking for other sites. I found something on Healthline. Just as with wikis, this should not be taken as the final, authoritative resource on this, but it should be enough to give you an idea of how this condition affects people.
There are two types of polycoria. These types are:
- True polycoria. You will have two or more separate pupils in one eye. Each pupil will have its own, intact sphincter muscle. Each pupil will individually constrict and dilate. This condition can affect your vision. It’s extremely rare.
- False, or pseudopolycoria. You have the appearance of two or more pupils in your eye. However, they do not have separate sphincter muscles. In pseudopolycoria, the holes in your iris look like additional pupils. These holes are usually just a defect of the iris and do not cause any issues with your vision.
The symptoms of polycoria are usually a product of having more than one set of iris muscles. The iris is the colored ring of muscle around each pupil. It controls how much light is allowed into the eye. In polycoria, the pupils tend to be smaller than normal and separated by individual segments of iris. This can mean less light enters your eye, which can dim your vision. You may also have difficulty focusing because the pupils aren’t working effectively.
The primary sign of polycoria is the appearance of two pupils. Other signs and symptoms may include the following:
- blurred vision in the affected eye
- poor, dim, or double vision in the affected eye
- oblong shape of one or all additional pupils
- issues with glare
- a bridge of iris tissue between the pupils
Some people with polycoria do not need any treatment because their vision is not affected enough to require it. For those whose vision becomes difficult because of the conditions, surgery is one possible treatment option. However, because true polycoria is so rare, it can be difficult to determine the best treatments for it.
One case study has shown that surgery was a successful treatment option. This type of surgery is called pupilloplasty. During a pupilloplasty the surgeon cuts through the tissue of the iris, getting rid of the “bridge” that has formed between the two pupils. The surgery, in this case, was successful and improved the patient’s vision.
So you see, true polycoria is more of a condition than an advantage for people.
I think this is not the answer you were looking for. If you want a fictional person or group of people to have a different kind of vision because they have compound eyes, you don't have to limit yourself to perfect, pedantic realism.
The description of an insectoid point of view and its pros and cons in fantastic/sci-fi literature is rare, but there are some examples nonetheless. My favorite one is from George R.R. Martin's Wildcards. One of the characters in the story, known as the Sleeper, one day mutates to have compound eyes. When faced with an enemy that is trying to kill him, Sleeper claims to see "two hundred sixteen [expletive]s". The enemy has the power to take someone's life by locking gaze with his victims, but on the Sleeper it fails because there are too many eyes to fix a stare on.
Another example is Dr. Baxter from the 80's TMNT cartoon. When he becomes an amalgamation of a human and a fly, his vision is shown as capable of tracking an object with many eyes at the same time.
One thing is for sure: if the person with multifaceted eyes has a human retina, they will, for all practical purposes, suffer from true polycoria. But if each eye has its own retina, then they have no blind spot, and effectively a super fovea. They could potentially have better lateral vision than most birds, which have a secondary fovea just for that.