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The incentive for using Evolutionary Algorithms (EAs) for the automated optimization and training of deep neural networks (DNNs), a process referred to as neuroevolution, has gained momentum in recent years. The configuration and training of these networks can be posed as optimization problems. Indeed, most of the recent works on neuroevolution have focused their attention on single-objective optimization. Moreover, from the little research that has been done at the intersection of neuroevolution and evolutionary multi-objective optimization (EMO), all the research that has been carried out has focused predominantly on the use of one type of DNN: convolutional neural networks (CNNs), using well-established standard benchmark problems such as MNIST. In this work, we make a leap in the understanding of these two areas (neuroevolution and EMO), regarded in this work as neuroevolutionary multi-objective, by using and studying a rich DNN composed of a CNN and Long-short Term Memory network. Moreover, we use a robust and challenging vehicle trajectory prediction problem. By using the well-known Non-dominated Sorting Genetic Algorithm-II, we study the effects of five different objectives, tested in categories of three, allowing us to show how these objectives have either a positive or detrimental effect in neuroevolution for trajectory prediction in autonomous vehicles.