You aren't missing anything. This is not standard French. It's likely that the writer started to phrase the sentence in a certain way and then changed it but didn't complete that change. For example, maybe the sentence was originally “… des évènements qui ont eu lieu en Lybie et qui ont eu …”, then the writer decided that “qui ont eu lieu” was uselessly wordy and removed it.
Or maybe the writer was just careless or hurried, and has this “qui ont eu lieu” in mind but didn't write it. The sentence as a whole has a bit of an informal feeling, with the use of on (instead of a definite subject) and the lack of a comma after “Dans le programme d'aujourd'hui”.
A more correct way to write this sentence would be
Dans le programme d’aujourd’hui, nous continuerons de parler des évènements en Lybie, qui ont eu beaucoup d’effet sur les pays de l’Afrique du Nord, le Moyen Orient et le monde entier.
“Nous continuerons” is correct if the author of the sentence is a participant in the program. If they aren't, then I think the sentence calls for naming the participants, or referring to them by some generic designation like “Pierre Durand et ses invités”.
The sentence is correct with and without a comma after Lybie, but leaving it out changes the meaning. With a comma, this is about “the events in Lybia” and the reader is supposed to already know which events the sentence is about; the part after the comma states an additional property of these events. Without a comma, “qui ont eu beaucoup d'effect …” specifies which events the sentence is about.
None of this matters very much to a native speaker. The sentence looks a bit odd, but there's no potential for misunderstanding.
