You might want to be a lot more specific about what date you are talking about. Is it the date inside the files in the EXIF? Is it the date in the name of the folder created by Lightroom? Is it some other date?
Most of the time, the date is determined by your camera, so you probably want to check to make sure your camera is showing the proper date.
Thanks for the reply. The camera date is accurate. However, when I import in LR and look at the date that is in the metadata, it is off by 1 day...
Since Lightroom does not change the date in the metadata unless you specifically tell Lightroom to do so, I still suspect the camera is off. Please check to see if the camera is off by 12 hours instead of 1 full day.
I just checked and the time on the camera is accurate. The metadata in lightroom appears off by 12 hours (for instance, something is showing up as being shot at 4 am, rather than 4 pm...
Camera set for the wrong time zone? Computer set for the wrong time zone?
The most effective way to troubleshoot this is to upload a sample pic to Dropbox (or similar) and then post the link here. We can then take a look at the pic's metadata and how it imports into LR.
I have exactly the same problem and it is totally messing-up my library. My camera is set to local time and my computer is set to local time. Yet is I open the Aug 10th folder it will have photos in it where the EXIF reads August 11th. I have changed nothing in my import settings. As you can see this is an Lightroom problem not a camera problem.
And at some point it saves later ones on the correct date. I this case JPEGs after 6pm were saved on the correct date but RAWS after 8 ??? totally weird. I'm running LR 5.6 most current version
Lightroom version: 5.6 
License type: Perpetual
Operating system: Mac OS 10
Version: 10.9 
Application architecture: x64
Logical processor count: 4
Processor speed: 1.7 GHz
Built-in memory: 8192.0 MB
Real memory available to Lightroom: 8192.0 MB
Real memory used by Lightroom: 1044.1 MB (12.7%)
Virtual memory used by Lightroom: 3089.7 MB
Memory cache size: 1756.0 MB
Maximum thread count used by Camera Raw: 2
Displays: 1) 1440x900
2) Canon Tether Plugin
3) DxO FilmPack 3
4) DxO FilmPack 3 (64-bit)
7) Leica Tether Plugin
8) Nikon Tether Plugin
Config.lua flags: None
AudioDeviceName: Built-in Output
GL_RENDERER: Intel HD Graphics 5000 OpenGL Engine
GL_VENDOR: Intel Inc.
GL_VERSION: 2.1 INTEL-8.28.30
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My camera is set to local time and my computer is set to local time. Yet is I open the Aug 10th folder it will have photos in it where the EXIF reads August 11th.
Are you importing from the camera using a USB cable? If so, that's a known bug, and the workaround is to import using a card reader or from a hard drive:
so no, I am importing with the built in card reader in the MacBook Air, so no cabled camera.
Hmm, if you upload one of the problem pics (August 11/10) to Dropbox and post a link here, we can take a detailed look and troubleshoot where the problem might be.