Concerns would arise from the following factors:
1: UV irradiation in the room the pieces are displayed in. I.e. natural light in said room.
2: Free radicals (e.g. ozone) in the air posing a threat to the dyes.
3: The influence of physical factors, esp. moisture and heat.
Re:1 - this can be addressed by a combination of framing behind UV-blocking materials (most perspex/Lexan does a fairly good job as most types have UV blockers incorporated) and simply hanging the frames in a spot where they receive no direct daylight and an overall low level of daylight to begin with. Evidently, limiting the time of exposure also helps.
Re:2 - this to an extent can be overcome again through competent framing, although it's rare for any type of framing to be truly impervious to air and contaminants. Use materials in framing that are suitable for archival purposes. Some materials can come with compliance data on a PAT (Photographic Activity Test), others materials can be deduced to be more or less inert based on their chemical composition. Deterioration will be affected obviously by air quality; i.e. it'll make a difference whether you're in the city or somewhere out in the country where the air is clear.
Re:3 - chemical processes obviously accelerate with heat, so try to avoid the display arrangement from getting warm. This is inherently problematic if you are going to mount these over a light source, although the heat in a typical LED tracing pad is generated only/mostly at the edge of the pad where the actual LEDs and their drivers are. Don't keep the LEDs on longer than necessary because of the heat they generate. The main concern w.r.t. physical factors however is moisture and the possible effective of ferrotyping the emulsion of the slides onto a framing material such as clear glass or perspex, which will be facilitated again by heat and moisture.
How deeply you want to be concerned by all of this depends a bit on how deeply you're attached to these slides. If you're OK with them degrading over time and would just like to enjoy them for a few years until you're basically done with them, then I wouldn't worry about all this too much. But if you want these slides to last for decades, you'll have to figure out the issues above. It could get kind of complicated if you want to play safe. Myself, I'd lean towards the former, but I tend to not get attached much to my photos.
