Lightrooms slideshow module unfortunately has rendering issues due to use of nearest-neighbor resampling algorithm for resizing images. This may or may not be what is causing your problem. Here's a procedure you can try using a few of the images that get "grainy." Please follow the instructions as outlined below for creating 1080p slideshows:
- Export the images to ‘Specific folder’ and ‘Rename to’ ‘Custom Name – Sequence’ to retain sort order.
- Use Export settings sRGB, 91 Quality, Width & Height 1539x1026, Sharpen for Screen Standard
- Open the above folder in the Library module and select Sort: ‘File Name’ to set correct sort order.
- In the Slideshow module select the ‘Widescreen’ template.
- Set Layout Guides (L, R, T, B) = 10, 10, 10, 44
- For 'Export to PDF' use Quality 91 and Width & Height 1559x1080
- For 'Export to Video' select '1080p' mode under Video Preset.
If this doesn't resolve the issue please provide the LR version you are using (4.3?) and camera ISO setting for the images.