LR writes the APP1 header as: TIFF header, 114 unused bytes, ExifIFD, IFD1, IFD0. Whereas Photoshop CC uses a more traditional layout: TIFF header, no unused bytes, IFD0, ExifIFD, IFD1. Here's an Exiftool dump of the beginning of a LR JPEG: And here's a dump of the beginning of a Photoshop JPEG: I've tested LR JPEGs with 12 Mac and Windows programs and 2 online services, all of which read them just fine:
Mac: Preview, Photoshop CC 2014, ColorSync Utility, Firefox, Chrome, Lattice, Paintbrush, Safari, Word Windows 8.1: File Explorer Preview, Irfanview, Paint, Windows Photo Viewer Online services: Flickr, Zenfolio
Even though LR's JPEGs may be strictly conforming, if it wrote the JPEGs without the unused header bytes and it put IFD0 immediately after the TIFF header, as Photoshop does, then there would be fewer problems with other programs choking on LR's JPEGs.