To understand what's going on here, it's useful to know a bit about how Lightroom handles your images under the hood.
When you import photos you may notice Lightroom telling you it's generating "previews". These are JPEG images, usually smaller than the full-size image you've imported, which Lightroom generates automatically and stores in its catalog database. It does this because it's subsequently much faster to load one of these JPEGs than to load up your original photo (especially if it's a RAW image) and re-apply all your edits before displaying it. The preview is updated whenever you apply a new edit to a photo, or you can force it to be re-generated from the menu (Library > Previews > ...). Whenever possible (for example, in the Library grid and loupe views), Lightroom will display the faster-loading preview rather than the original RAW image, hence making the experience of browsing through your catalog a bit more slick and responsive.
The blotchy sky you're seeing in the comparison with Windows image viewer is because your previews are set to low or medium quality: this generates smaller JPEGs which load quicker at the expense of some compression artefacts. To fix that, just go to Edit > Catalog Settings... > File Handling and set the preview quality to High. You may want to change it back if you notice this slows Lightroom down appreciably.
I also see the noise issue you've described, and I can always fix it by zooming in to the full-size view of the image (in the Develop module) then back out again. The problem seems to be that the zoomed-out version of the image just update properly when you make noise adjustments.