I could not reproduce it on regular desktop with Intel CPU.
Not sure platform is related, but who knows ....

This is small zabbix server running on a RaspberryPi Model B (512 MB RAM).

# cat /proc/cpuinfo
processor       : 0
model name      : ARMv6-compatible processor rev 7 (v6l)
BogoMIPS        : 2.00
Features        : half thumb fastmult vfp edsp java tls
CPU implementer : 0x41
CPU architecture: 7
CPU variant     : 0x0
CPU part        : 0xb76
CPU revision    : 7

Hardware        : BCM2708
Revision        : 000e
Serial          : 00000000dc8125bb

# cat /etc/debian_version
7.8
# cat /etc/issue
Raspbian GNU/Linux 7 \n \l
# uname -a
Linux kot2 4.1.7+ #817 PREEMPT Sat Sep 19 15:25:36 BST 2015 armv6l GNU/Linux
# mysql -V
mysql  Ver 14.14 Distrib 5.5.46, for debian-linux-gnu (armv7l) using readline 6.2

Zabbix server is compiled on this host from sources and running with mysql server (innodb_buffer_pool_size = 128M).
Regular 32GB SD card is used as a hard drive.
Raspbian linux is up to date.
Zabbix trunk versions 3.0.0+ are always running on this host, sometimes recompiled.

I've noticed some SQL errors in zabbix_server.log, could not understand why they appear.
I'm 99% sure that such SQLs were missing for example 5 months ago when this small zabbix installation was rolled out based on some revision of trunk (3.0.0+).

To make a clean test I've created a fresh mysql database (based on trunk r57353), unlink&clear "app zabbix server" template, set 2 discovery rules (from "Template OS Linux") scheduled update interval to m/1 (just to be sure when LLD rules are executed), but SQL errors still are appearing.

  3016:20151223:183401.036 [Z3005] query failed: [1062] Duplicate entry '350-23663' for key 'items_applications_1' [insert into items_applications (itemappid,applicationid,itemid) values (5893,350,23663),(5894,350,23664),(5895,350,23662),(5896,350,23665);]
  3016:20151223:183401.159 [Z3005] query failed: [1062] Duplicate entry '347-23667' for key 'items_applications_1' [insert into items_applications (itemappid,applicationid,itemid) values (5893,347,23667),(5894,347,23669),(5895,347,23666),(5896,347,23668),(5897,347,23670);]

Taking into account that I cannot reproduce it on my Intel CPU workstation - I suppose that something is wrong with zabbix server daemon on ARM platform.

Attached server log file shows those SQLs when debug level was 3 and also when level was increased to 4 for single running poller.

p.s. when this zabbix server is running with "production" database - server logs additional SQL error, related to lld graph elements creation for missing items, but I guess it has the same nature.
They are probably relates to new network interface recently added to this host and started to be discoverable.

9193:20151222:182758.445 [Z3005] query failed: [1452] Cannot add or update a child row: a foreign key constraint fails (`trunk`.`graphs_items`, CONSTRAINT `c_graphs_items_2` FOREIGN KEY (`itemid`) REFERENCES `items` (`itemid`) ON DELETE CASCADE) [insert into graphs_items (gitemid,graphid,itemid,drawtype,sortorder,color,yaxisside,calc_fnc,type) values (1849,554,23748,5,0,'00AA00',0,2,0),(1850,554,23749,5,1,'3333FF',0,2,0);]