I'd looked for leading spaces, but not for non-display characters. It seems that this is the problem (Thanks Tulrose). I've gone back and looked at the names again, and I think it may be that they are the people who were added by merging sources through the web search function.
Is anyone aware of a way to fix this without having to change each name manually?
I have tried to get the index to sort. If I'm trying to find a person to switch to their record, there is an option to sort by name (which will work, but needs to be resorted every time) but there is no way to have this happen when you're trying to link to an existing source. Luckily I have split my family tree into four parts to keep the size down and haven't brought the rest into FTM 2014 as yet.
I will log this as a bug. I'd not been able to find a web page to use for this, so thanks for putting the link up, silverfox3280.