Setup a master-slave replication, m1->s1 with RBR.

In m1 do the following init operations:
1. create table table without pk

create table t(c1 int,c2 int);

2. insert the following test data:

insert into t values (1,1),(2,2),(3,3),(4,4),(5,5),(1,1),(2,2);

3. check the data on m1 and s1, will see the result sequence is the same:

Then start the test:
1. do the following update on m1

update t set c2=rand()*100 where 1=1;

2. check the data on m1 and s1, will see the result sequence is different:

On m1
mysql> select * from t;
+------+------+
| c1   | c2   |
+------+------+
|    1 |   43 |
|    2 |   23 |
|    3 |   87 |
|    4 |   65 |
|    5 |   63 |
|    1 |   21 |
|    2 |   17 |
+------+------+
7 rows in set (0.01 sec)

On s1
mysql> select * from t;
+------+------+
| c1   | c2   |
+------+------+
|    1 |   21 |       <====== the result sequence is different with master
|    2 |   17 |
|    3 |   87 |
|    4 |   65 |
|    5 |   63 |
|    1 |   43 |
|    2 |   23 |
+------+------+
7 rows in set (0.01 sec)

3. add auto_increment as pk on m1

alter table t add column id int auto_increment primary key;

4. re-check the data in m1 and s1, we will see the data in-consistence 

On m1
mysql> select * from t;
+------+------+----+
| c1   | c2   | id |
+------+------+----+
|    1 |   43 |  1 |
|    2 |   23 |  2 |
|    3 |   87 |  3 |
|    4 |   65 |  4 |
|    5 |   63 |  5 |
|    1 |   21 |  6 |
|    2 |   17 |  7 |
+------+------+----+
7 rows in set (0.01 sec)

On s1
mysql> select * from t;
+------+------+----+
| c1   | c2   | id |
+------+------+----+
|    1 |   21 |  1 |   <===== the row with id=1 is different with the master
|    2 |   17 |  2 |
|    3 |   87 |  3 |
|    4 |   65 |  4 |
|    5 |   63 |  5 |
|    1 |   43 |  6 |
|    2 |   23 |  7 |
+------+------+----+
7 rows in set (0.01 sec)

4. Do the following update on m1

update t set c2=c2*10 where c1=1 and c2=43;

5. re-check the data in m1 and s1, we will see the data serious in-consistence

On m1
mysql> select * from t;
+------+------+----+
| c1   | c2   | id |
+------+------+----+
|    1 |  430 |  1 |       <==========c2 is update from 43 to 430 as expect
|    2 |   23 |  2 |
|    3 |   87 |  3 |
|    4 |   65 |  4 |
|    5 |   63 |  5 |
|    1 |   21 |  6 |
|    2 |   17 |  7 |
+------+------+----+
7 rows in set (0.01 sec)

On s1
mysql> select * from t;
+------+------+----+
| c1   | c2   | id |
+------+------+----+
|    1 |  430 |  1 |     <======the update in slave replay on the wrong row
|    2 |   17 |  2 |
|    3 |   87 |  3 |
|    4 |   65 |  4 |
|    5 |   63 |  5 |
|    1 |   43 |  6 |     <======it should update this row
|    2 |   23 |  7 |
+------+------+----+
7 rows in set (0.01 sec)