I am holding an Engineer Visa in Japan that is expiring in June. I have changed my job since February and did not immediately notify immigration. After reading posts on this site, I sent notification via E-notification. Could this late notification affect my visa extension?
It is not clear that you will have any problems regarding the date of this notification. You are required to give notification, but it does seem that as long as you do so, there will be no negative repercussions as regards to your current status. Your job was consistent with the work you were originally given the visa (and Certificate of Eligibility) for. Since you've honored the spirit of your original visa and even provided the notification, I believe this will likely be considered a positive in your future applications (not so fast, see edit below).
edit: I've added a link here which is the best English description. There are plenty of sites that state what I state (I've basically paraphrased), and forums with people whose own accounts are consistent with this.
Here is another anecdote from a failed extension (who did notify in time!). Seeing that, I would definitely recommend looking into getting a certificate of authorized employment to be on the safe side.
If you did not apply for a Certificate of Authorized Employment before changing companies, there could be problems. See my second link. This certificate isn't required (if the translation from the official Japanese immigration site is accurate), but it is highly recommended apparently. I don't know if you are eligible to apply for this now that you have already started your new employment (though it is implied that you can). You may want to contact a specialist.
edit 2: I'm providing another link to fkraiem's related answer on the punitive measures. Doesn't discuss future extensions, but may give you some peace of mind as far as your current status is concerned.