Try asking for a date, not a document id.
var current = Meteor.videos.findOne(currentID);
Previous:
Meteor.videos.find({date: {$lt: current.date}}, {sort: {date: -1}, limit:1});
Further:
Meteor.videos.find({date: {$gt: current.date}}, {sort: {date: 1}, limit:1});
You also need to sort the next cursor in ascending order.
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