If you do not convert a vacation scheme, I'd encourage you to ask the firm whether it is worthwhile reapplying. There won't be a general view of how firms will look at this - it very much depends from candidate to candidate. For the same firm, I have actively encouraged someone to reapply the next cycle as they narrowly missed out (and I thought they could easily improve their development areas) while for another candidate, I encouraged them to not reapply because I didn't think their motivations were going to change (and we couldn't offer them the career they truly wanted).
I'd say open days are generally easier to secure as they don't rarely have a formal recruitment process to them (e.g. no face-to-face interviews or assessments). However, open days can still be competitive to get on to for this reason. The application process tends to be a little more straight forward and therefore more people can apply. How competitive an open day or vacation scheme is though can be really varied, even for things outside of the firm's control. I have seen different programmes receive very different applications from year to year just because competitors were running schemes on the same dates, or because a deadline changes by a couple of weeks.
You can include deals in applications, but most importantly you don't have to. There are many other ways to demonstrate your interests and your research. If you do reference a deal, you have to ensure whatever you are referencing has meaning/relevance to you and your application. Just naming a deal and saying "this is the type of work I want to do as a trainee" is not specific enough. What is it specifically about that deal over others you could have chosen? Referencing a deal is okay to do if it is naunced and tailored to you. However, deal name dropping (just throwing it in for the sake of showing some research) should be avoided.
I just had two questions re interviews:
