My daughter started doing this a few months ago, she was about 20 months. I was talking to my mother-in-law and was telling her the all about how we reached the terrible twos already. She turned and said 'call then the trying twos and the twos will be a lot easier.' If you change your perspective on the situation it may help.
First I made sure that there was nothing else bothering her at her 20 month checkup. The doc said she is very aware and smart so she needs safe choices
She likes to make her own decisions so I give her 2 choices with everything unless it something that she has no say in (like holding my hand in the parking lot). That way she feels she has a say and that I am listening, which makes the situations where she has no say easier because she knows I would let her chose if there was a choice. The choices I offer are like do you want to wear the purple skirt or pink shorts, or do you want water or milk... this way she feels she has the choice but I control the choices but offering only 2. If it is going from the car to house, and it is safe, I usually ask my daughter to carry something inside for me (her cup, fuzzy bear, or book) that way she is on a mission.
Tantrums in public I find more trying no me, I hate making a scene but most people who have/had kids understand so I try to not worry about it. If I am in the store say we have to get food and she can help find what we need... if this does not help and can put of the shopping then we leave or if we have a lot of items in the cart I buy what we have and leave ASAP. But often I cannot put off the shopping trip so I find a corner in the store where I put the cart and let her run her course (she is sitting in the cart facing a wall and I stand on the other end of the cart). If I am at a mall or clothing store I put everything down and leave, more then likely those trips don't need to be done then.
If there are tantrums at home she is set in a corner in her room to cry/scream it out. I tell her when she is done she may get up, it took a few times for her to understand that I am serious. If she got up and complained, cried etc at me I sat her right back in the same corner. Now if she starts a tantrum I tell her to go sit down and she goes to her corner... but after a few months of doing this she rarely has a big tantrum. Getting enough sleep is also very important as the other moms have said. For nap I leave her in there till she has actaully taken a nap, some times she plays for an hour before finally falling asleep but she needs to sleep and knows I won't get her till after she actaully naps.
Best of luck to your neighbor, it is a trying time but remember that it is not a terrible time. 2 year olds want to try everything so create safe situations for him to chose from. Also instead of saying just no explain why it is a no otherwise they have no idea why you are saying no and are more likely to do the same thing over and over again.