Ayu`s English is fine. I don`t know if it`s improving but I think her English is fairly good. But I do have to admit, in "Real Me" song I would`ve never got that "in oder to survive" part if I hadn`t read the lyrics.

I was just listening to LOCE ~since1999~ and the bit where she goes "I cried for you, and you cried for me" is acutally really good. And also in the 30sec Mr. & Miss Dohnut CM where ayu is the man her English is excellet! She says "Thanks" perfectly! Usually it comes out "Sanks"

Every promise is, every moment is, but I was holding on for my love...

I think that's it...

As for her worst, I love Heartplace, but I had the hardest time realizing that she was saying "We are free to go anywhere we want, we are free to do anything we want" Over was just annoying. "I can't smile without you... I always will love you... IT'S OHHHHHHVERRRRRRRRRR" @_@ That's a good way to kill my ears... it's even worse as a remix... X_x

There is a Cm where she sings White Christmas....
that sound OKAY , too

LOVE since 1999 is tsunku's work. And the lyrics are halfway engrishy.

The "th" sound is really difficult if you haven't been brought up with it, a lot of non native speakers have problems with it, even people who know perfect english (except for pronounciation).

best:

Bold & Delicious
Real me

worst:
LOVE ~since 1999~
forgiveness

BEST:

Bold & Delicious (Dang, without BOLD & DELICIOUS screaming out at you, you wouldn't feel the energy of the song)
Real me (LOL, the Engrish is what characterizes the song)
Beautiful Fighters (We are Beautiful Fighters!)
Ladies Night (Oh my, rather somewhat incomprehensible English rapping, BUT it really gives the song a quirky edge)
Heartplace (One of my favourite album tracks on the RAINBOW album. Not particularly strong english, but rather strong on emotions. Thought that the English brought it out nicely.)

WORST:

Over ("It's OVERRRR!" -- Geez, absolutely HORRIBLE. The rest of the song is rather ok though)
forgiveness (It doesn't help to include english at this juncture when it's TRULY incomprehensible.)
LOVE ~since 1999~ ("I cry for you and you cry for me", "what colour is true love", ok, but I think tsunku did the lyrics for this. Bah, I really dislike the song)

the english words in forgiveness is at its worst

Everywhere Nowhere was GOOD english to me, int he beginning. WE WISH, was okay, real me okay...they both i could understand fine, but her accent was kinda strong back then. BnD was awesome english. BF....well, it's good. BnD was still better. When she sang Silent Night....omg.
i love how she uses her english most of the time, it's just a matter of understanding it...i'm pretty good at understanding accents though.