If you follow all their security measures you will not any face any problems. I am using it to store my ERC20 coin in MEW. It is very convenient for me to store all my books in one place.
Let say you follow all thier security measures but suddenly thier website got hacked . what can you say to that ? Didnt you faced any problem ? There is right ? in the online world , there is no perfect or safest wallet/website because all of them are all prone to hacks and other maliscous threats . you will never know when will badluck strikes so better prepare and brace your self for the unexoected . meanwhile , the best thing to do is to bookmark the legit mew site because there is an issue of phishing attacks lately .