When improvising, which I am not good enough at to perform without a fair amount of rehearsal, I often do quite well, but do make some vary glaring mistakes. I have to play over a progression quite a few times before I am ready to perform (in front of a live audience).
It sounds like you're saying 'I have to practice a lot or else I make glaring mistakes'. This is normal. Some people make things sees effortless but it really because they already expended tons of effort in the past already.
I would also like to improve my ability to identify chord progressions. I recognize some simple progressions when I hear them, but need improvement. I often cannot identify simple progressions.
Getting better at this will help you with improvisation greatly so I'll offer recommendations to help with this.
In order to improve with hearing progressions the easiest thing you can do is look at chord progressions for pop songs. Sites like Ultimate Guitar make this extremely easy.
Look at the chords written down and identify their number, eg No woman no cry's progression is
C G Am F
C F7 Am7 D9 C
It is in C major, so the numbers would be
I, V, vi, IV
I, IV, vi, II, I
Once you have it on paper you are ready to listen to the song. I -> V has a certain sound to it regardless of the key. Get familiar with it. Listen to the song on and try to hear when the I -> V movements happen.
Next, G -> Am is V -> vi. Another super commom move. Listen out for that.
Realise that I -> V -> vi is the same as Pachelbel's canon. Realize that a huge portion of pop music could basically be played along with Pachelbel's canon. Internalize the sound of I -> V -> vi. Hear it in every song, it is important.
Look for other songs that kinda fit. (Realize that pop music is basically just one long song. - optional)
The key here is to read, learn the chord progressions concretely first, then listen for the characteristic sounds of different movements. After a while the movements stand out in your ear. Especially the common ones. Once the common movements sounds obvious you can go on to try to anticipate them in strange songs. The patterns are really predictable. Once you do what I described above you get you'll be able to intuit correct chord changes on most pop songs on your first or second try after a few weeks.
After that soloing is a matter of getting into the right chord shapes on the guitar and playing around. This is what scales are for. If you learn a few of the scale shapes as well as how to hear the chords you'll have a very firm foundation to improvising and soloing. Everything beyond this point is up to the style of music you are looking to play.
Kinda long post but I hope this helps.