Not wanting to clutter the vote thread, nor knowing what to report as a bug I am hoping to get some hints on what to look at first,
AND also requesting a command-line example to test iconv - as there seems to be an issue around this when using the default
iconv programs on AIX.

make check of apr-util-1.5.1 returns:
testdate            : SUCCESS
testmemcache        : SUCCESS
testxml             : SUCCESS
testxlate           : |/bin/sh[17]: 10879096 Segmentation fault(coredump)
Programs failed: testall
make[1]: *** [check] Error 139
make[1]: Leaving directory `/data/prj/apr/apr-util-1.5.1/test'
make: *** [check] Error 2

root@x104:[/data/prj/apr/apr-util-1.5.1/test]dbx testall core
Type 'help' for help.
[using memory image in core]
reading symbolic information ...

Segmentation fault in . at 0xd21c1110 ($t1)
0xd21c1110 (???) 901e0000         stw   r0,0x0(r30)
(dbx) where
_iconv_from_utf8(??, ??, ??, ??, ??) at 0xd21c1110
iconv(??, ??, ??, ??, ??) at 0xd054aff8
apr_xlate_conv_buffer() at 0xd18f6084
test_conversion() at 0x10008d7c
one_test() at 0x10008c8c
test_transformation() at 0x100089dc
abts_run_test() at 0x10001484
testxlate() at 0x10008e28
main() at 0x100004f8

Not knowing if it has anything to do with the apr it is running with (using 1.4.6 as that is latest release, rather than against core).

apr-1.4.6 make check returns:
testrand            : SUCCESS
testsleep           : SUCCESS
testshm             : SUCCESS
testsock            : FAILED 1 of 9
testsockets         : SUCCESS
testsockopt         : SUCCESS
teststr             : SUCCESS
teststrnatcmp       : SUCCESS
testtable           : SUCCESS
testtemp            : SUCCESS
testthread          : SUCCESS
testtime            : FAILED 1 of 13
testud              : SUCCESS
testuser            : SUCCESS
testvsn             : SUCCESS
Failed Tests            Total   Fail    Failed %
testsock                    9      1     11.11%
testtime                   13      1      7.69%
Programs failed: testall
make[1]: *** [check] Error 1
make[1]: Leaving directory `/data/prj/apr/apr-1.4.6/test'

Also not perfect and will investigate, with assistance, time permitting.
Note: no rush for me - willing to spend time to get it right.