Question: Home Depot/Lowes, etc., have boiled linseed oil at a much cheaper price than the local art store that I go to.

Are there any problem using boiled linseed oil from these home stores for oil painting applications, cleaning brushes etc?

Answer: 
The thing about the art store options is that they're being tested by the manufacturers for their impact on the longevity of the painting or color impact to the pigments, so I would divide my response into a couple of parts...

Brush Cleaning? Sure, presuming that you're doing additional cleaning after. If you're looking to just store the brushes in the oil, between sessions, I would be more hesitant.

Painting? I would pass on it. It may well be perfectly fine, depending on the brand, but as I noted, they're likely not testing for your use case. At the end of the day, if you're looking to make works that last, going too cheap comes with risk. However, all that goes out the window with student grade paint options. If you're already taking a skip on the longevity, then I don't think you're really risking anything here either.

Finally, you can always test it yourself. Just don't do it on anything you care about until you know.
To reduce the potential effects of yellowing/browning, I use hardware store BLO only with dark colors. I use only art store BLO for light colors. If you don't mind diluting colors with boiled linseed oil, go for it. It works great on the abstract stuff, usually the very large-sized works.

If you do indoor painting, use walnut oil, instead, which has the least odor of them all.

Never use paint thinner to clean brushes indoors. Refined mineral spirits from art stores may have less odor, but the fumes can still be hazardous to your health.

You can use baby oil to clean the brushes indoors. But make sure not to paint with baby oil. Dip the brush in linseed oil a few times and wipe before using it again.

As an aside, the best tip I have for oil painters is buy the orange grease-removing soap/cleaner sold at automotive stores. It cleans the grease mechanics suffer with, and it does a great job on cleaning your hands with oil paint.