It carries tremendous disadvantages.
In fact, I'm quite surprised that at this late date, with a greater understanding of what it means to force your citizens to use the Deutsche Mark, that they have made this decision.
With all due respect to Croatia and the lovely people that live there, they cannot compete globally with Germany in any interesting export market.
The typical tool that a nation uses to deal with that reality is the relative value of their currency. Consumers of import goods then have a choice to make between German quality and (for instance) Spanish pricing.
... and now that lever will be gone.
At this point I think it is fairly well understood what the economic - and social - ramifications of this are and, again, I am actually quite surprised they've made this choice.