With straightforward use of -target 1.8, there aren't many limitations to begin with. Spring 3.2.13 even includes the latest ASM 5.0.3 in the meantime, so it's fully up to date at that front. The only part worth noting is the AspectJ version: If you happen to be using AspectJ and in particular load-time weaving, there may be issues on Java 8 unless you upgrade to AspectJ 1.8.5; however, Spring 3.2.13 just supports AspectJ 1.7.4 - we haven't tested it with AspectJ 1.8.x at all.
Beyond that, Spring 3.2.x simply doesn't include any dedicated Java 8 support: i.e. no JSR-310 date-time, no parameter discovery via -parameters, etc. If you don't intend to rely on those features initially, that's by no means a showstopper. I would just strongly recommend an upgrade to Spring 4.x as soon as you intend to embrace Java 8 more fully. For the time being, using Spring 3.2.13 on Java 8 will get you quite far and is entirely safe for your purposes.
Note that we'll release 3.2.14 in May, as a minimal maintenance release, so that line is still actively supported for the time being. There's also a 3.2.15 release planned towards the end of this year, again designed as a very minimal maintenance release. Please be prepared that the 3.2.x line will fade out at that point, with its eventual end of life to be expected for mid/late 2016 and in all likelihood just one further maintenance release (3.2.16) to appear until then.
Hope that helps,