Every component is overloaded with default styles. Customizing them to fit into your design is very difficult. The process starts with removing the unnecessary styles and then adding your own. Sometimes you'll have to use !important to get rid of default CSS properties.
12 Columns Grid System is not a perfect grid system. Even though they claim to vertically divide the screen into 12 equal columns, it doesn't make any sense when implemented for mobile screens. The content won't fit into these columns and hence they will stack on top of each other.
Forms and default height for input elements. Some input fields have height properties pre-defined. You'll go crazy when you have to increase padding.
Lack of communication from the Bootstrap team. Unlike other companies like Zurb Foundation, Bootstrap's creators are arrogant and have very poor communication skills. It maybe because of the extra undeserving fame they have got for their bloated framework.
You can make your own version when you compile the source code. Bootstrap is made in SASS, which makes you able to do it just by changing variables to fit your needs. You can even change the number of grid columns.
Go here. Use col-xs-6 etc. to divvy up mobile view. You could also use the link above to change the number of columns, or even use LESS after the fact.