Drop-down compatibility issue between computers - all have Excel 2013

Hi there,
I've created a "Furniture Request Form" (FRF) using Excel 2013 that is distributed to partner agencies with which they provide necessary information about clients they are referring to our business. My problem is that at least one of the agencies complains that 1) not all of the drop-downs appear on their version of the form, and 2) the screen flickers every time they enter data in one cell and tab/click to the next cell. Today I went to the agency to troubleshoot the problem but am now stumped. My first thought was that they were using Excel 2007 or earlier, but they had Excel 2013 loaded on both computers I tested. My next assumption was that their computers lacked processing power or memory and, while that might be true of one computer (Windows 7 SP1, 1 GB RAM, 32-bit, i3 processor), it was not the case for the other (Windows 8, 4 GB RAM, 64-bit, i5 processor 2.4GhZ), yet the exact same problem was expressed on both computers.

The file that is provided to the agencies is an Excel Template without any macros. It has been distributed to over 20 agencies in 2015, and I have only noticed problems with this particular agency (it is evident because without the drop-down options their limits aren't restricted, and there are some other "word-text" values on the first page that they complete with the wrong words).

The form has one main sheet (FRF) and one data validation sheet. The data validation sheet contains most data for drop-down columns that have more than 3 options. There are two pages on the FRF - the first is for residential and contact information, family composition and demographics; the second is simply a list of household items offered in one column and drop-down lists of numbers in the next column. The maximum # of each item a household (HH) may request is determined by the HH size. For instance, if a HH has 4 residents the maximum number of beds that could be requested is 4, and the drop-down would read: "1,2,3,4,0,0,0,0". If there were 8 in the HH, though, the drop-down would read: "1,2,3,4,5,6,7,8". These outcomes are generated based on calculations from the data validation page, and the base numbers for the calculations is pulled from page 1 of the FRF.

The odd thing is that some of the drop-down lists work while most of them don't. I didn't think to explore whether the lists that DO work are short lists that I typed into the "Data Validation" tab as opposed to drawing the options from the Data Validation sheet, but I suspect that might be the issue. I do not understand, though, why the other drop-downs are not recognized.

I had the staff send the document they use back to me so I could play with it, and I had no errors (however, I used the computer the form was created on - mine; I will try it on a couple of other computers tomorrow). I know that there are compatibility issues between Excel 2007 and 2010, but I have not heard of such issues between two different computers running the same version of software.

Any ideas as to what the issue might be? I have found some suggestions for the flickering screen, but nothing about this specific compatibility problem.

Thanks much!

Thank you all for your feedback. I will suggest the other agency try some of the advised solutions. I believe I used pretty common fonts (likely Calibri as that's default) and didn't utilize any special characters, but I will go back and check. Thank you for the link. Also, I will try to attach a file (I actually spent some time trying to pare down the file to remove unnecessary info last night, but then realized that the problem wouldn't likely mimic itself on other computers) a bit later today. After some reading I have a feeling it might have to do with the drivers installed or installation of the software itself. Will let you know, though!
Thank you for the warm welcome.