Further investigation showed that this is with Tramp only.
Can anyone reproduce on GNU Emacs, particularly 23 CVS?

Begin forwarded message:

> From: Ian Eure <ian.eure@gmail.com>
> Date: 23 June 2008 23:22:39 BST
> To: aquamacs-bugs@aquamacs.org
> Subject: [Aquamacs-bugs] ~ and / behavior in find-file changed
>
> Enter your bug report here.
>
> It used to be that when I typed a / or ~ in the minibuffer after find-
> file, the current path would be grayed out, and the resulting path
> would be treated as absolute. No longer; I must delete the current
> contents to type an absolute path in Aquamacs 1.4.
>
> In GNU Emacs 22.2.50.2 (i386-apple-darwin9.2.2, Carbon Version 1.6.0)
>  of 2008-06-17 on plume.sr.unh.edu - Aquamacs Distribution 1.4
> Windowing system distributor `Apple Inc.', version 10.5.3
> configured using `configure  '--without-x' '--prefix=/usr/local''
>
> Important settings:
>   value of $LC_ALL: nil
>   value of $LC_COLLATE: nil
>   value of $LC_CTYPE: nil
>   value of $LC_MESSAGES: nil
>   value of $LC_MONETARY: nil
>   value of $LC_NUMERIC: nil
>   value of $LC_TIME: nil
>   value of $LANG: nil
>   locale-coding-system: iso-8859-1
>   default-enable-multibyte-characters: t
>
> Major mode: JavaScript-IDE
>
> Minor modes in effect:
>   erc-track-mode: t
>   erc-track-minor-mode: t
>   erc-spelling-mode: t
>   erc-ring-mode: t
>   erc-pcomplete-mode: t
>   erc-netsplit-mode: t
>   erc-match-mode: t
>   erc-autojoin-mode: t
>   shell-dirtrack-mode: t
>   yas/minor-mode: t
>   erc-button-mode: t
>   erc-fill-mode: t
>   erc-irccontrols-mode: t
>   erc-noncommands-mode: t
>   erc-readonly-mode: t
>   erc-scrolltobottom-mode: t
>   iswitchb-mode: t
>   auto-insert-mode: t
>   savehist-mode: t
>   smart-frame-positioning-mode: t
>   recentf-mode: t
>   encoded-kbd-mode: t
>   osx-key-mode: t
>   tabbar-mwheel-mode: t
>   tabbar-mode: t
>   show-paren-mode: t
>   delete-selection-mode: t
>   pc-selection-mode: t
>   cua-mode: t
>   tooltip-mode: t
>   mouse-wheel-mode: t
>   menu-bar-mode: t
>   file-name-shadow-mode: t
>   global-font-lock-mode: t
>   font-lock-mode: t
>   blink-cursor-mode: t
>   unify-8859-on-encoding-mode: t
>   utf-translate-cjk-mode: t
>   auto-compression-mode: t
>   size-indication-mode: t
>   column-number-mode: t
>   line-number-mode: t
>   transient-mark-mode: t
>   abbrev-mode: t
>
> Recent input:
> SPC M-( w i n d o w . l o c a t i o n . M-b M-b M-f
> M-f C-f s u b s t r SPC <backspace> M-( w i n d o w
> . l o a t i o n . r <backspace> i n d e x O f M-( M-'
> . M-b C-d L <backspace> l a s t I C-e C-b M-m M-d C-d
> a l s r <backspace> <backspace> e r t C-e ; C-x C-s
> C-b <down-mouse-1> <mouse-movement> <mouse-1> C-f i
> n g M-< C-s s u b s t r C-s C-s i n g C-s C-s C-s C-v
> C-b C-b C-b C-b C-b C-_ C-n C-p C-n C-p C-b C-b C-p
> C-p C-p C-p C-p C-x C-s <down-mouse-1> <mouse-1> <right>
> <M-return> a l e r t M-( w i n d o w . l o c a t i
> o n C-e ; C-x C-s <down-mouse-1> <mouse-1> C-d . <backspace>
> / C-x C-s C-p C-c C-k <tab> M-f C-f C-f C-f C-f C-f
> C-f C-f C-f C-f C-f C-f C-f C-f C-f C-f C-f C-f C-f
> C-f C-f C-f C-f C-f C-f C-f C-f C-f C-f C-f C-f C-f
> C-f C-f c C-x C-s M-b M-b M-Z M-) <M-return> a l e
> r t M-( C-y C-e ; C-SPC C-a C-p C-w C-n <tab> <tab>
> M-f M-f M-f M-f C-f M-Z ) C-p <tab> l a <backspace>
> <backspace> a l e r t M-( C-y C-e ; C-x C-s C-x C-f
> ~ / P r <tab> d i <backspace> <backspace> <tab> <tab>
> <tab> <tab> <tab> <backspace> <backspace> <backspace>
> ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ C-a C-k ~ /
> C-g <menu-bar> <help-menu> <send-emacs-bug-report>
>
> Recent messages:
> Saving file /ssh:dev01.digg.internal:/home/ieure/legocat.dev.digg.internal/html/js/comments.js
> ...
> Wrote /ssh:dev01.digg.internal:/home/ieure/legocat.dev.digg.internal/html/js/comments.js
> zap-to-char: Search failed: "=a9"
> Mark set [2 times]
> syntax error
> Mark set [2 times]
> Saving file /ssh:dev01.digg.internal:/home/ieure/legocat.dev.digg.internal/html/js/comments.js
> ...
> Wrote /ssh:dev01.digg.internal:/home/ieure/legocat.dev.digg.internal/html/js/comments.js
> ad-Orig-error: Not a tramp file name: ~/Pr [6 times]
> Quit