Your situation sounds similar to mine. DD is 4 years old (was 3 when we separated). XWW and I also share 50/50 legal custody.
The custody plan that works best will depend on a variety of factors. Your geographical proximity to one another will be a big factor (I've experienced all sorts of headaches related to this). Take an honest look at both of your schedules, and be sure that you can actually realistically do 50/50. XWW and I are 50/50 on paper, but in reality, I'm with my daughter closer to 70% of the time. If this doesn't change, I'm going to try to push for a modification of our custody arrangement so that I can actually have primary custody, because while I do enjoy having more time with my daughter, I do not enjoy lacking any of the legal privileges associated with being the primary parent. If you think something like that might happen (let's say your spouse travels a lot, for instance. That is something that might create an imbalance), try to get that sorted out now so it saves you another trip to the courthouse later on.
Another big headache that I wish I had avoided relates to school districts. Again, this depends on how close you and your STBX live to one another, but I've had no end of stress related to this issue with my ex who lives 40 minutes away. If I had been able to have my address designated as her primary address for schooling, I would have saved myself a lot of anxiety.
I'm only a year in, but these are some of the things that I already wish I had done differently. There are other long-range things you might want to think about as well, such as how college expenses will be handled. It seems crazy to plan something like that in advance, but a general rule is that you want to have as many things in writing as you possibly can. If your XWW tries to convince you that you can just wing it and that such-and-such doesn't need to be so meticulously spelled-out, don't listen. You might be cooperating decently now, but if things go to shit later on, you'll want to make sure your rights are clearly spelled-out.
With regard to taxes, we alternate years claiming DD as a dependent. That seems pretty common. Our 2013 return was actually a joint return since our divorce wasn't final until January. XWW agreed to let me handle the taxes for this last joint year. It made things a little less complicated. But that only really works if you're getting divorced at the end of the year.
When it comes to the OM... Gosh. I am so sorry that you have to deal with that. Absolutely nothing made my skin crawl more than the idea of XWW's AP being around my daughter, and thankfully they broke up, but with that possibility in mind, I was able to sneak something into the agreement that was meant to protect DD in the case of that eventuality. Basically it said that, with the exception of close relatives, anyone who was going to be left alone with DD had to be approved by the other parent. Ostensibly this was aimed at babysitters. So, for instance, any time I hire a new babysitter to watch DD, I have to inform XWW and get her approval. But theoretically, this could have applied to the OM as well. Now whether this would have been enforceable or whether it would have stood up to any kind of challenge in court if the two of them decided to get married or anything like that, I don't know, but it gave me a certain measure of comfort knowing that clause was in the agreement. I have no idea if this will work for you.
I'll say a prayer to whatever vengeful gods take care of people like us that your STBX and the OM won't be together for long.
As for joint outings... I have no doubt that DD would enjoy it, but in my estimation it's a bad idea. I think Gemini71 already expressed very well why this is. And even if you can handle it emotionally (I don't think I could), I don't think it's sustainable, and you'd only be postponing the heartbreak when your daughter finally does see you split up in a more complete way.
I do miss experiencing my daughter with someone that I love, but I don't love XWW anymore. And I do grieve that my daughter has lost the chance to experience things with the three of us as a family, but we are not a family anymore. XWW made sure of that. She now has two families. This is the new normal for her, unfortunately.
In spite of this loss, the time that I have with my daughter is precious beyond measure, and our bond has grown stronger since the divorce. Yes, your daughter will probably miss having her mommy and daddy together, and knowing that will be hard to endure, but she will also appreciate all the new time when she can have you all to herself. She doesn't have to share you with anyone anymore. When you are with her, she has your undivided attention. It might spoil her a bit, but she'll appreciate it.
I hope some of this helps. Hang strong.