The easiest way but worst way I can think of to do that would be to pick a code point that’d new to each Unicode release, and check its Character properties. Or you could check its General Category with a regex. Here are some selected code points:

Unicode 6.0.0:

Ꞡ  U+A7A0 GC=Lu SC=Latin    LATIN CAPITAL LETTER G WITH OBLIQUE STROKE
₹  U+20B9 GC=Sc SC=Common   INDIAN RUPEE SIGN
ₜ  U+209C GC=Lm SC=Latin    LATIN SUBSCRIPT SMALL LETTER T

Unicode 5.2:

Ɒ  U+2C70 GC=Lu SC=Latin    LATIN CAPITAL LETTER TURNED ALPHA
‭⅐ U+2150 GC=No SC=Common   VULGAR FRACTION ONE SEVENTH
⸱  U+2E31 GC=Po SC=Common   WORD SEPARATOR MIDDLE DOT

Unicode 5.1:

‭ꝺ  U+A77A GC=Ll SC=Latin    LATIN SMALL LETTER INSULAR D
Ᵹ  U+A77D GC=Lu SC=Latin    LATIN CAPITAL LETTER INSULAR 
⚼  U+26BC GC=So SC=Common    SESQUIQUADRATE

Unicode 5.0:

Ⱶ  U+2C75 GC=Lu SC=Latin    LATIN CAPITAL LETTER HALF H
ɂ  U+0242 GC=Ll SC=Latin    LATIN SMALL LETTER GLOTTAL STOP
⬔  U+2B14 GC=So SC=Common  SQUARE WITH UPPER RIGHT DIAGONAL HALF BLACK

I've included the general category and the script property, although you can only inspect the script in JDK7, the first Java release that supports that.

I found those code points by running commands like this from the command line:

% unichars -gs '\p{Age=5.1}'
% unichars -gs '\p{Lu}' '\p{Age=5.0}'

Where that’s the unichars program. It will only find properties supported in the Unicode Character Database for whichever UCD version that the version of Perl you’re running supports.

I also like my output sorted, so I tend to run

 % unichars -gs '\p{Alphabetic}' '\p{Age=6.0}' | ucsort | less -r

where that’s the ucsort program, which sorts text according to the Unicode Collation Algorithm.

However, in Perl unlike in Java this is easy to find out. For example, if you run this from the command line (yes, there’s a programmer API, too), you find:

$ corelist -a Unicode
    v5.6.2     3.0.1     
    v5.8.0     3.2.0     
    v5.8.1     4.0.0 
    v5.8.8     4.1.0
    v5.10.0    5.0.0     
    v5.10.1    5.1.0 
    v5.12.0    5.2.0 
    v5.14.0    6.0.0

That shows that Perl version 5.14.0 was the first one to support Unicode 6.0.0. For Java, I believe there is no API that gives you this information directly, so you’ll have to hardcode a table mapping Java versions and Unicode versions, or else use the empirical method of testing code points for properties. By empirically, I mean the equivalent of this sort of thing:

% ruby -le 'print "\u2C75" =~ /\p{Lu}/ ? "pass 5.2" : "fail 5.2"'
pass 5.2
% ruby -le 'print "\uA7A0" =~ /\p{Lu}/ ? "pass 6.0" : "fail 6.0"'
fail 6.0
% ruby -v
ruby 1.9.2p0 (2010-08-18 revision 29036) [i386-darwin9.8.0]

% perl -le 'print "\x{2C75}" =~ /\p{Lu}/ ? "pass 5.2" : "fail 5.2"'
pass 5.2
% perl -le 'print "\x{A7A0}" =~ /\p{Lu}/ ? "pass 6.0" : "fail 6.0"'
pass 6.0
% perl -v
This is perl 5, version 14, subversion 0 (v5.14.0) built for darwin-2level

To find out the age of a particular code point, run uniprops -a on it like this:

% uniprops -a 10424
U+10424 ‹𐐤› \N{DESERET CAPITAL LETTER EN}
 \w \pL \p{LC} \p{L_} \p{L&} \p{Lu}
 All Any Alnum Alpha Alphabetic Assigned InDeseret Cased Cased_Letter LC Changes_When_Casefolded CWCF Changes_When_Casemapped CWCM Changes_When_Lowercased CWL Changes_When_NFKC_Casefolded CWKCF Deseret Dsrt Lu L Gr_Base Grapheme_Base Graph GrBase ID_Continue IDC ID_Start IDS Letter L_ Uppercase_Letter Print Upper Uppercase Word XID_Continue XIDC XID_Start XIDS X_POSIX_Alnum X_POSIX_Alpha X_POSIX_Graph X_POSIX_Print X_POSIX_Upper X_POSIX_Word
 Age=3.1 Bidi_Class=L Bidi_Class=Left_To_Right BC=L Block=Deseret Canonical_Combining_Class=0 Canonical_Combining_Class=Not_Reordered CCC=NR Canonical_Combining_Class=NR Decomposition_Type=None DT=None Script=Deseret East_Asian_Width=Neutral Grapheme_Cluster_Break=Other GCB=XX Grapheme_Cluster_Break=XX Hangul_Syllable_Type=NA Hangul_Syllable_Type=Not_Applicable HST=NA Joining_Group=No_Joining_Group JG=NoJoiningGroup Joining_Type=Non_Joining JT=U Joining_Type=U Line_Break=AL Line_Break=Alphabetic LB=AL Numeric_Type=None NT=None Numeric_Value=NaN NV=NaN Present_In=3.1 IN=3.1 Present_In=3.2 IN=3.2 Present_In=4.0 IN=4.0 Present_In=4.1 IN=4.1 Present_In=5.0 IN=5.0 Present_In=5.1 IN=5.1 Present_In=5.2 IN=5.2 Present_In=6.0 IN=6.0 SC=Dsrt Script=Dsrt Sentence_Break=UP Sentence_Break=Upper SB=UP Word_Break=ALetter WB=LE Word_Break=LE _X_Begin

All my Unicode tools are available in the Unicode::Tussle bundle, including unichars, uninames, uniquote, ucsort, and many more.

Java 1.7 Improvements

JDK7 goes a long way to making a few Unicode things easier. I talk about that a bit at the end of my OSCON Unicode Support Shootout talk. I had thought of putting together a table of which languages supports which versions of Unicode in which versions of those languages, but ended up scrapping that to tell people to just get the latest version of each language. For example, I know that Unicode 6.0.0 is supported by Java 1.7, Perl 5.14, and Python 2.7 or 3.2.

JDK7 contains updates for classes Character, String, and Pattern in support of Unicode 6.0.0. This includes support for Unicode script properties, and several enhancements to Pattern to allow it to meet Level 1 support requirements for Unicode UTS#18 Regular Expressions. These include

The isupper and islower methods now correctly correspond to the Unicode uppercase and lowercase properties; previously they misapplied only to letters, which isn’t right, because it misses Other_Uppercase and Other_Lowercase code points, respectively. For example, these are some lowercase codepoints which are not GC=Ll (lowercase letters), selected samples only:

% unichars -gs '\p{lowercase}' '\P{LL}'
◌ͅ  U+0345 GC=Mn SC=Inherited    COMBINING GREEK YPOGEGRAMMENI
ͺ  U+037A GC=Lm SC=Greek        GREEK YPOGEGRAMMENI
ˢ  U+02E2 GC=Lm SC=Latin        MODIFIER LETTER SMALL S
ˣ  U+02E3 GC=Lm SC=Latin        MODIFIER LETTER SMALL X
ᴬ  U+1D2C GC=Lm SC=Latin        MODIFIER LETTER CAPITAL A
ᴮ  U+1D2E GC=Lm SC=Latin        MODIFIER LETTER CAPITAL B
ᵂ  U+1D42 GC=Lm SC=Latin        MODIFIER LETTER CAPITAL W
ᵃ  U+1D43 GC=Lm SC=Latin        MODIFIER LETTER SMALL A
ᵇ  U+1D47 GC=Lm SC=Latin        MODIFIER LETTER SMALL B
ₐ  U+2090 GC=Lm SC=Latin        LATIN SUBSCRIPT SMALL LETTER A
ₑ  U+2091 GC=Lm SC=Latin        LATIN SUBSCRIPT SMALL LETTER E
ⅰ  U+2170 GC=Nl SC=Latin        SMALL ROMAN NUMERAL ONE
ⅱ  U+2171 GC=Nl SC=Latin        SMALL ROMAN NUMERAL TWO
ⅲ  U+2172 GC=Nl SC=Latin        SMALL ROMAN NUMERAL THREE
ⓐ  U+24D0 GC=So SC=Common       CIRCLED LATIN SMALL LETTER A
ⓑ  U+24D1 GC=So SC=Common       CIRCLED LATIN SMALL LETTER B
ⓒ  U+24D2 GC=So SC=Common       CIRCLED LATIN SMALL LETTER C

The alphabetic tests are now correct in that they use Other_Alphabetic. They did this wrong prior to 1.7, which is a problem.
The \x{HHHHH} pattern escape so you can meet RL1.1; this lets you rewrite [𝒜-𝒵] (which fails due to The UTF‐16 Curse) as [\x{1D49C}-\x{1D4B5}]. JDK7 is the first Java release that fully/correctly supports non-BMP characters in this regard. Amazing but true.
More properties for RL1.2, of which the script property is by far the most important. This lets you write \p{script=Greek} for example, abbreviated as \p{Greek}.
The new UNICODE_CHARACTER_CLASSES pattern compilation flag and corresponding pattern‐embeddable flag "(?U)" to meet RL1.2a on compatibility properties.

I can certainly see why you want to make sure you’re running a Java with Unicode 6.0.0 support, since that comes with all those other benefits, too.

How to identify programmatically in Java which Unicode version supported?

Java 1.7 Improvements