What is the difference between 看法 and 想法? Both can mean "view/idea/opinion". 

For example, I can say: 
对这个问题有两种不同的看法 (there are two different view on this question)

Would it be reasonable to replace "看法" with "想法"?
Think about a scenario: You and your group are asked to do a social survey, and you're going to pick up your topic by yourselves. So you called a meeting to discuss it. Everybody talked about their ideas(想法), and you vote for a topic. 
Think about another scenario: At class, your professor played a piece of video about some hot news, and then he wanted you to talk about your own point of view(看法).
So, "想法" is usually used when there is some problem need to be discussed to solve. "看法" is usually used when people talked about their opinions about something happened or some social phenomenon.
"想" means you need to think and "看" means how you see this.
Yet in daily life, replace one with another won't make it a big deal, so people sometimes don't take the difference seriously, they just speak it out.
May this would help.