LogFAQs > #934240497

Yep, you're certain to miss out on social links (unless you use a guide), but none of them except the aforementioned Marie link are anything more than extra characterization and scenes. As far as actual game content goes, the ending splits are the only way to miss things and those are discrete and singular branching points that you won't miss.

If you want to do all the social links, your options are to use a guide or to grind up your social stats on a first playthrough and carry them over to NG+ to do all the links there. But, again, you're not missing huge amounts of content by missing out on them.