What is wrong with my batch file?

I am using this: start java.exe -Xmx1024M -jar josm-%downloadFileVersion%.jar and it works.
Your problem might be that java directory is not in PATH (try writng set PATH). Add it to PATH or use full path for java (C:Program Files...java.exe).

The whole starting script:

@echo off
rem default settings

set downloadFileVersion=tested
set runTracerServer=true

rem read parameters
:Loop
IF "%1"=="" GOTO Continue

    echo %1
    GOTO %1

    :/latest
        set downloadFileVersion=latest
        goto :END_SWITCH

    :/noupdate
        goto runapps

    :/notracer
    set runTracerServer=false
        goto :END_SWITCH

    :/help
        echo:JOSM starter script
        echo:starts JOSM tested or latest version, updates the program if needed. 
        echo:keeps all settings in the directory from where it was started
        echo:run [/latest] [/notracer] [/help] [/noupdate]
        echo:    /latest    runs latest version instead of tested
        echo:    /notracer  does not run tracer server
        echo:    /help  displays this help
        echo:    /noupdate  does not run update, any parameters after this one are ignored
        goto end

    :/?
    goto /help

    :-?
        goto /help

    :-help
        goto /help

    GOTO END_SWITCH
    :END_SWITCH
SHIFT
GOTO Loop
:Continue

echo:Setting up settings + plugin location
set APPDATA=appdata
echo:set to %APPDATA%

echo:Determining actual %downloadFileVersion% version number (server)
curl http://josm.openstreetmap.de/%downloadFileVersion% -verbose -o %downloadFileVersion%.txt
set /p serverVersion=<%downloadFileVersion%.txt

echo:Determining current version
java.exe -Xmx1024M -jar josm-%downloadFileVersion%.jar -? | findstr /C:"Revision" > current.txt
set /p temp=<current.txt
set currentVersion=%temp:~10,4%

echo Server %downloadFileVersion%: %serverVersion%
echo Local %downloadFileVersion%: %currentVersion%

set /a diffVersion=serverVersion-currentVersion
echo Difference: %diffVersion%

if %diffVersion% == 0 (
    echo:JOSM is up to date 
    goto runapps
) else (
    echo:Update or downgrade needed
)

echo:Downloading latest version
rem Download to temporary file, then copy and remove - to prevent file corruption when download fails
curl http://josm.openstreetmap.de/download/josm-%downloadFileVersion%.jar -o josm-%downloadFileVersion%-download.jar
rem todo - check download success
move /Y josm-%downloadFileVersion%-download.jar josm-%downloadFileVersion%.jar
del josm-%downloadFileVersion%-download.jar

:runapps

echo:Starting JOSM 
start java.exe -Xmx1024M -jar josm-%downloadFileVersion%.jar

if %runTracerServer% == true (
    echo:Starting tracer server
    start TracerServer\bin\Osm.Kn.Trace.Server.exe
)

rem pause

rem Delete temporary files
del %downloadFileVersion%.txt
del current.txt

:end

LM_1 has provided an interesting, if lengthy batch file. Mine, on 64 bit Windows 7, simply reads:

C:\Windows\SysWOW64\java -Xmx1500m -jar C:\Users\Ed\Downloads\JOSM\josm-latest.jar

Which I think is "using the full path" as he suggested:

There is a YouTube tutorial video of CMD and Java,

link

i hope it helps you...

In answer to this question:

'But this begs the question: Why, if I buy a new computer with 6GByte of RAM, can`t I get more than 512MByte allocated. -Xmx1024m functioned on my old computer with 2GByte of RAM. Could it be that my RAM is defect?'

I suspect that you need to use the 64-bit Java.exe not the 32-bit one. On my (Windows 7, 4Gb) PC 32-bit Java fails to start JOSM with 1.4Gb max allocated, but 64-bit Java has not problem with 3Gb.

Your 32-bit version of Java is probably installed in somewhere like:

"c:\Program Files (x86)\Java\jdk1.6.0_32\bin\"
(also available via) "c:\windows\syswow64\"

Your 64-bit version of Java is probably installed in somewhere like:

"C:\Program Files\Java\jre6\bin\"

Try using that to start JOSM instead.