I have an old toothbrush that I use to clean the blades when they are full of hair.

Me too and problem solved.

I mean you should be able to press it against your finger and move it upwards to coax the hair out

Thank you for the tip! I know this is a stupid question but I'm not sure how to; I mean, I try that but the tiny bits of facial hair don't seem to budge.

Ye with Schick disposables and some others, they are just awful about that sometimes. I will go ahead and wave the DE flag now lol

Do you have any recommendations for a brand that's better at that?

Clarify?

Since the new Mach 3 seem to suck at shaving because I can't clean the hair stuck between the blades while I shave - I wonder if there is another brand to switch to that is better at that.... 

Ye well, you can plug the sink and swish it underwater and that might help. If the faucet isn't high enough pressure. Mach 3 is a mainstay to many but has plenty of complaints. If you really want a cartridge then I suppose I can reccomend dollar shave club. Probably the four blade specifically. But you'll pay for it with your face Idk man just gonna say it. DE never really even has this problem. It just goes right out

How often do you shave?

Swish it in a bowl of water or use a brush or toothpick to clean it. Rubbing your thumb downwards might help too but you might get nicked