Regarding the question of splitting area 1 across the backbone (area 0):
[area 1, subnet 1]---[ABR #1]---[area 0, subnet 2]---[ABR #2]---[area 1, subnet 3]
[area 1, subnet 1]---[Router #1]---[area 0, subnet 2, end device #1]---[Router #2]---[area 0, subnet 2, end device #2]---[Router #3]---[area 1, subnet 3]
Short answer: There is no problem with your proposal...
Even Peter's answer, which argues that reusing area numbers is bad design, offers no proof that this is a bad design; if you examine the hyperlinks he used, there is no explanation of undesirable consequences for this design. Furthermore, the argument that you might have problems connecting R1 and R3 falls short, since the R1 to R3 link could legitimately be configured in either Area 0 or Area 1, depending on what traffic you want to transit it. The difficulties he mentions are a false dilemma.
In RFC 2328, Section 3.7 OSPF explicitly allows you to use discontiguous non-backbone areas (which are called "area partitions", below):
OSPF does not actively attempt to repair area partitions. When
an area becomes partitioned, each component simply becomes a
separate area. The backbone then performs routing between the
new areas. Some destinations reachable via intra-area routing
before the partition will now require inter-area routing.
... Also, the backbone itself must not partition.
Thus whether you use the proposed discontiguous Area 1 is just a matter of taste... some people find it illogical to use the configuration in your diagram; these people might suggest that you keep OSPF area numbers together... so you'd have to change [area 1, subnet 3] on Router #3 to [area 3, subnet 3]. Other people see no problem with reusing Area 1, since OSPF area numbers are only locally significant to the router originating OSPF hellos.
Either way, we should admit that OSPF is a remarkably flexible protocol; regardless of choosing one side or another in this debate.