The only thing they need to do make the CGI 10x more palatable is make the colour grading more natural. I became aware of this when I read in an Empire Magazine interview with Peter Jackson: he was talking about how, on set, flesh-coloured dwarf prosthetics had to be bright red, and tree bark needed to be purple and blue, because otherwise the processing would make them look wrong. They didn't - as far as I know - have that problem before orange and teal became the standard movie look.
While 90% of Jurassic Park's dinosaurs look perfect, some bits - close ups of the CGI raptors, the gallimimus stampede, the brachiosaur's skin - look pretty ropey now. But they're coloured naturally, and so the whole scene looks more real, even if the dinosaur itself looks a bit ropey. In Jurassic World, the excessive colour grading makes the entire world look fake, so the dinosaurs themselves have no chance to blend in.
Another, easily fixable problem with CGI monsters is that animators always make them move too cartoonishly. As a kid, I remember clocking that one of the things that made Jar Jar stick out was all the little flourishes he did - bobbing on his heels, exaggerated swallowing and breathing, googling his eyes - and that one of the things that made Gollum so convincing was that he didn't perform any of these flourishes. In real life, animals breathe, eat, and look around without making particularly visible movements, or without their skin bulging in and out, sagging and stretching.
We've swung right back to the Jar Jar approach, and Jurassic World is a perfect example. The film opens with a baby raptor hatching, and its fingers drum across the surface of the egg and twitchily flick away pieces of it. In Jurassic Park, when we see the baby raptor being born, it's a puppet, and its fingers move and flex clumsily and slowly - like a newborn, tiny creature's would. In Jurassic World, the I-Rex's nostrils flare, its head twitches, its entire body bobs up and roils as it moves; in Jurassic Park, the T-Rex's body isn't rigid, but its body and tail are largely tense, like a creature in motion would be.
TLDR: We've had the means to make CGI creatures look totally great for a decade - it's the way its animated and coloured that's the issue.