Does changing the theme "mid-way' affect a wordpress website in any way? Say for instance, if a website is getting decent traffic, will the traffic or SERPs get affected? I understand that if I add a bad theme it can affect for the worse, but what about an equivalent or better theme?
If your content is strong and you have enough autority backlinks, changing a theme will barely change anything, UNLESS the change of theme has big impact on the user experience of the website, link structures, sitemap etc. This will definitely change things yeah...
I've been running plenty of sites in the past and yes, I did experience drops or gains in SERPs when I changed the layout.
BUT, let me emphasize that these were all custom coded websites, so the whole code changed, I changed the internal linking structure somewhat, sometimes I even moved it to another host etc... so the changes I made were quite big.
If we're talking about a simple change of a wordpress theme, I tend to agree with stickupkid... given that you keep everything else as is, the impact shouldn't be big.
I was recently doing some research when it comes to how much of an effect themes have on SEO. The general consensus seems to be that the theme alone has some impact on the overall SEO performance of a site, but it's not the biggest factor by far.
Some themes are better optimized in terms of SEO, due to their loading speed, the structure of the content pages (H tags, labeling, code quality) and so on. However, the usage of a proper SEO plugin seems to be a more important part.
To sum it up, if you happen to switch from a well optimized, fast loading and properly structured theme to a poor one, the SEO results might suffer somewhat. But if you are using a good SEO plugin, have strong content and backlinks, it shouldn't be a tragedy.
@jeremie @matuloo Thanks for sharing!
And if you're displaying ads, another concern (in addition to affects on SEO rankings as others have pointed out) may be a potential change in ad performance.
I had a wordpress site that was making 4-figures/day in ad revenue on what I thought was a crappy theme I chose on a whim while setting up the site. Since it was making money I thought "why not test other themes to try to maximize earnings?"
And every theme is a little different in where ads can be displayed.
Ended up: I tested quite a few other themes, and none of them performed remotely as well as the original one. One of the themes even decreased the ad revenue by 90%. Needless to say, I eventually reverted to the original theme.
Even if you're not displaying ads: Whatever else you may be selling/promoting, do be careful and watch that CTR and CR. Site design can have a considerable impact on those metrics.
Not to mention: If you have visitors that have been visiting your site regularly, any major or jarring change will have a potential to annoy people - because not everybody likes change.
Amy
When I'm thinking about this now, what Amy mentioned above should probably be of bigger concern than the SEO effect.
I remember a situation where we changed the design on a popular local website we owned and the people literally went NUTS. Let me say that the old design was horrible, bad choice of colors, confusing layout etc... so we basically made it much better, but since people were used to the old design they suddenly felt lost with the new one and totally rejected it. There was a forum attached to the site and people posted MANY angry threads about how we fucked it up, how they hate the new layout and how they're going to stop using the site... eventually, we had to revert to the old one and gave them the option to switch to the new one voluntarily. It was quite a lesson for sure.
@vortex @matuloo Helpful indeed!
Yeah not exactly the SEO effect ( possibly indirect effect on SEO too), but it seems to be the best option to find a theme of choice and stay with that. 
Keep the internal linking structure the same!
If rankings go down, revert back to the "old" design.
Then you should be fine!
@matuloo Cheers!