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: 
My understanding is that the art store stuff is better filtered and cooked differently.

I read that the main risk is early yellowing-browning....that being said I have used it in the past and I have paintings done 15-20 years ago using very liberal oil amounts (painting in layers, glazes: a very small amount of pigment diluted in a lot of oil), and i haven t noticed any color shifts or browning.

I think that if you use small amounts of oil or if you sell your paintings it's safer to stick to the art store type.
If you use a lot of oil, and as you mentioned for cleaning brushes, and the end result isn't critical, then sure do it.

( side note :I feel there is too much emphasis on "archival", last 100's of years, do it right or don't bother, from so many painters when the sad truth is that their paintings are extremely unlikely to survive them, if they even make it that far, while some artists can paint using Mayonaise and if they are great, there will always be ways to preserve their work)

( And side-side note, most of the museum grade classical painting were painted using crap, there was no quality control and no purification or controlled manufacturing processes, the pigments were often unevenly grounded full of impurities, unstable, mixed with bad oils and additives and some ingredients used were organic and decayed...for instance Indian Yellow was most likely made from the urine of Indian cows on a diet of mango leaves, Wikipedia has a good article on it....moreover some of the things we admire in classical paintings are actually due to "improper" conservation and "faulty" mediums)

Edit: just realized this is a very old question, though it was new. anyways, hope it helps.
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.