Every online store is unique. Every store has some specific demands. But it doesn't mean we're clueless when we just start working and when we're not familiar with the particular store's demands yet. There's a list of typical demands that make sense all the time.
Lighting
Despite the fact that photographers are originally responsible for all the lighting problems, the moment we pass our images to quality control, whatever's wrong with them is our fault. Even the lighting and other on-stage issues, such as:
Correct exposure. The images should be neither too dark, nor too bright.
Consistent lighting (no dark-to-light gradients or other issues of poor lighting).
No loss of information in the shadows and highlights, clipping control (dark parts of the images should not be totally black, and vice versa with the light parts of the images, but there are some exceptions to these: glares on metal, saturated colors that can’t fit the RGB range, some specific materials like latex etc)
Adequate contrast (not too bleak and not too contrasted)
Correct white balance (which is very important for color reproduction)
No parasitic tints (which can happen not due to the wrong WB, but because some colored objects were present during the shooting, like a photographer’s bright red t-shirt or something like this)
All-kinds-of-items demands
The first rule from this list is very important. Sometimes different product images come from different photo stands, like a mannequin stand and a model stand, and the result might be a bit different. Even the same photography stand can produce slightly different results from image to image. When the difference is evident and can be perceived easily, it should be corrected by the retoucher:
Multiple photographs of the same item should not look much different. There's nothing more confusing to clients than this.

If objects are supposed to be aligned according to some guidelines, they should be aligned precisely. Sticking out or falling behind the margins is not acceptable.
It’s also very important that all the images are in focus and sharp. It's not that important on model images, especially when the model is shot from afar, but in detail shots it's vital.
As for the close-ups, it should also be evident which material the product is made of, otherwise, the image itself is meaningless. Remember it when your crop your images.
The products as well as models should be standing straight and not be leaning to any of the sides.
There should not be any dust, scratches, hair or anything like that on the products.
There should not be any traces of such things being removed by means of retouching, too.
The products should not bear any unnatural wrinkles due to the lack of preparation.
On the other hand, natural wrinkles are perfectly okay and should not be removed, as the items will look unnatural otherwise.
Black materials should not be too black, otherwise the customers won’t be able to see any details.
Same with white materials, which should not be too bright or too dark as well.
There should be no attached labels. Labels sewn in place should not be removed. Huge labels that are sewn in place but will most probably be removed by the customer can be removed during the retouching process.
Images should not be covered in moire, be it colored or monochrome.
Now, when we are familiar with all the basic demands of the industry, let's also get acquainted with specific demands, that are only applicable to particular kinds of images. They cannot be applied to just any online store, as there are no isolation demands if you're not isolating, and there are no ghost mannequin demands when you don't have a single mannequin in your studio.