All bioinformatic applications, including mapping (to a FASTA), will proceed as usual. For annotation, you'll also be fine as long as the contig/scaffold names are the same as the annotation file you're using. This isn't a major problem - the human reference, for example, has a number of unlocalized scaffolds and patch scaffolds that are relevant for annotation but aren't in the set of more thoroughly characterized chromosomes. Contigs/scaffolds/chromosomes are often treated the same by most applications.
So, to answer your questions:
Not really, but realize that your analysis may be impacted if all the scaffolds can't be localized to true chromosomes (e.g., are two scaffolds in LD because they're next to each other in reality?).
Outlined above, but they're generally captured under issues resulting from 'assembly uncertainty' sensu lato.