Welcome to FT! This is not a mistake (on your part) - this is a system flaw/error and often middle name and surname (or first name) is written without space. Not an issue at all. Check-in agents are used to deal with it.

Absolutely nothing to worry about, i.e. you will be able to travel as it is. Anyone telling you to buy a new ticket must be out of the mind/do not know how it works in reality.

Next time, skip the middle names. First and last name will suffice.