The next days after learning a kanji I usually miss the reading. I don´t know if I should be doing something better to try to remember the reading when doing the lesson
My accuracy is:
Kanji: Reading 78% meaning 89%
Vocabulary: reading 83% meaning 89%
Usually my accuracy is the worst near the start of a level too. For some kanji it just takes a while before they stick. I don’t really see it as a problem, you get them back quite soon so you’ll see them a few times until you recognize them, that’s just how an SRS works.
Seems to depend on my state of mind as well. Being tired doesn’t help - they just don’t stick!
Some of them just make no sense until I adjust a mnemonic. I do admit I don’t do any extra work to learn them but have been thinking I should do that!
Your percentages look like mine 
I usually find that really picturing the mnemonic in my head, and maybe even acting it out a wee bit helps. That way when the kanji comes up in a review, I can picture the same image I did during the lesson and follow the same thought path to get from radicals to meaning to reading.
My percentages are typically mid 90s, so I guess it works for me. 
I found this depended on which level I was on. Some levels were definitely harder than others. At times it was pretty smooth sailing. Either way, it doesn’t really matter. It’s just good to do a couple of failures in the beginning so you get to see those new items more times. 
Whenever I learn kanji from lessons, (generally I do all/most at once), I use the self-study script and run through all the kanji until I get them all right three times in a row. Helps solidify and send them up more reliably.
I don’t use any outside studying (apart from seeing it in things I’m reading) after that self-study, so if I fail at any point after that, I let it fail.
How do you know what your accuracy is?
I know that for some I have a difficult time because they look so similar and I miss them until I realize they are two different ones. Ex, right and stone. They both kept popping up because one was a review and one was new. Until I figured that out I kept missing both. 
I also get the ones mixed up between the pink screen and the blue screen. I learn the kanji screen and then it becomes a different reading on the blue screen and it messes me up and then when a new vocab word comes around and used the kanji instead of the new vocab I get messed up. Its taking a lot sometimes for me to differentiate when to use which one. I rarely use the mnemonic on here as some of them really don’t make sense to me. I normally come up with my own and type that into the notes section as well as what I have to type in to get it right. Like YOU have a TASK to do today, or MIGIt it RIGHT next time. I know they sound stupid but they help me. 
Is the self-study script something extra on here?
wkstats.com gives you the accuracy and some other useful stats
Also, this is a great tool when you confuse the kanjis 
Yup…just happened, failed quite a lot from the kanji I learned yesterday xD
That was extremely helpful!!! Thank you!!!
Yes, it’s a API add-on script you can find in the API section on the forum.
After taking lessons (and also reviews) Wanikani displays a summary page when the icons for all items in the lesson are displayed. I go over these items an recite the readings and meanings aloud. Then I move the mouse over the item icon. This reveals the correct answers in a popup. I have found this extra studying improves the retention and accuracy.
I also study the recent lessons in Self-Study Quiz. This requires to install the Addition Filters script on top of Self-Study Quiz. This causes additional filters to be available in Self Study including a filter for recently taken lessons. Without the additional filters there is no way to be quizzed on just the lessons.