In short: Go for it, but watch it with romance theme in mind, not time-travel.
Being a Time-Travel anime (it's in the genre so I don't think it's a spoiler) this anime sure has many plot-holes but, if you are expecting too much out of a Shoujo manga whose main theme is romance and not time-travel, then it's on you. Nevertheless, there was enough explanation so that it doesn't leave you hanging on this aspect.
The concept was somewhat new for me, which is a breath of fresh air and there were many elements that you can't see coming. Though it is cliché in places, but that much is ok. It does its part of delivering the romantic drama feels perfectly. The characters are memorable, you won't forget them like other 13-episode-anime characters.