As stated in the comment: generally ISRs should take steps to prevent reentrancy. In something like a PIC, this could be as simple as disabling the interrupt at the "top" of the ISR, and enabling the interrupt at the "bottom". The M3's NVIC is a bit more complicated. This white paper (http://www.arm.com/files/pdf/IntroToCortex-M3.pdf) states the following on p.7:
The NVIC supports nesting (stacking) of interrupts, allowing an
interrupt to be serviced earlier by exerting higher priority. It also
supports dynamic reprioritisation of interrupts. Priority levels can
be changed by software during run time. Interrupts that are being
serviced are blocked from further activation until the interrupt
service routine is completed, so their priority can be changed without
risk of accidental re-entry.
The above discussion directly addresses the possibility of same interrupt reentrancy, and it also introduces the concept of prioritization to handle interrupts of higher priority interrupting your ISR.
This reference is pretty good: http://infocenter.arm.com/help/topic/com.arm.doc.dui0552a/DUI0552A_cortex_m3_dgug.pdf. On p. 4-9, you'll find instructions to enable/disable interrupts. On page 4-6, you'll find a description of the Interrupt Clear-pending Registers. Using these, you can determine what interrupts are pending. If you really want to get fancy with interrupt enable/disable control, check out the BASEPRI and BASEPRO_MAX registers.
Having said that, I'm not sure I agree with your statement that your question is relevant to any Cortex-M3. Keil (my flavor of Cortex-M3) mentions that the EXTI (external interrupt controller) handles GPIO pin interrupts. Interestingly, the ARM documentation briefly discusses "EXTI", but does not refer to it as a "controller" like the Keil STM32 documentation. A quick google on "STM32 EXTI" yeilds lots of hits, a similar search on "Luminary EXTI" does not yield much. Given that, I'm guessing that this particular controller is one of the peripheral devices that ARM leaves to 3rd parties.
This document
bolsters that view: http://www.st.com/internet/com/TECHNICAL_RESOURCES/TECHNICAL_LITERATURE/REFERENCE_MANUAL/CD00171190.pdf. There are several AFIO_EXTI registers mentioned here. These permit the mapping of GPIO lines to interrupts. Unfortunately, I can't find anything similar in the Luminary documentation.
So...what does this mean? It looks like you only have port-level granularity for your interrupt. Thus, your ISR will have to determine which pin transitioned (assuming your are looking for edges). Good luck!