First, please restart the computer if you haven't already done so since you noticed the problem. That might be all you need to do.
Otherwise, select one of the items in question in the Finder and open the Info window. If the Modified date is January 24, 1984, see below.
Back up all data before proceeding.
Select the text on the line below by dragging across it. Don't include the blank space at the end of the line. Only the text should be highlighted.
touch -t 198001010000
Copy the selected text to the Clipboard by pressing the key combination command-C.
Launch the Terminal application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
Paste into the Terminal window by pressing command-V, then press the space bar.
Now switch to the Finder and and select all the item(s) in question. If there are thousands of items, only select a hundred or so. Drag into the Terminal window. More text will be added to what you entered.
Click in the Terminal window to activate it, then press return.
Wait for a new line ending in a dollar sign ($) to appear. You can then quit Terminal.
Relaunch the Finder. You should now be able to access the files as usual. The modification dates will still be inaccurate, but they'll be corrected the next time you modify the files.