This would not only make your 'date' think of you to be less compatible, but it will also make him/her believe that you may still and even in the future, would think about your exes. You're starting something good altogether and the last thing needed is to jinx it with some bad experiences you may have had in the past.
And God forbid if you do happen to be late due to any XYZ reasons, please be more than honest about the situation, the other person is more likely to understand and take such things more positively if you do so. This would ensure that you prioritize this date above other things, in simpler words, this person above other things. Until & unless your house is on fire, or there is an emergency, you should be showing up on time. Being late, on the other hand, would surely be a no-no on the first date. Time is of great importance to everyone and punctuality shows that you really care and hold your 'date' to be important enough. And although, predicting the future is still a futuristic thing, yet there are ground rules you can lay to cover the major possible contingencies, by not doing what's stated below! From the difference in opinions to a bad taste at dressing up, there can be a number of things that can go wrong on a first date.
Your entire plan of action is like a house of cards that can collapse even over a single conversation that she or he wouldn't agree upon. First Dates are like those unchartered territories where everything can go wrong in an instance.