[MC-40343] Vanilla server reports "Can only throw Throwable objects" on startup

I downloaded the server 1.7.2 jar from the minecraft.net site, tried to fire it up, and got the following:

$ java -Xmx1024M -Xms1024M -jar minecraft_server.jar nogui
Exception in thread "main" java.lang.VerifyError: (class: net/minecraft/server/MinecraftServer, method: v signature: ()V) Can only throw Throwable objects

(The file was named minecraft_server.1.7.2.jar when I downloaded it; I tried renaming it; creating a symlink to it, etc. – it doesn't seem to affect the result; also, I tried reinstalling Java, but that didn't change anything, either.)

One other tidbit: when I try to start the client, I get the conjugate error,

Exception in thread "main" java.lang.VerifyError: (class: ban, method: f signature: ()V) catch_type not a subclass of Throwable at net.minecraft.client.main.Main.main(SourceFile:72)

I tried the 1.6.4 server jar, and it hits this problem:

...
2013-11-16 23:01:58 [INFO] Preparing spawn area: 11%
java.lang.NoSuchFieldError: b
	at abw.a(SourceFile:1982)
	at abw.c(SourceFile:2002)
	at abw.A(SourceFile:1964)
	at abw.f(SourceFile:308)
	at afm.a(SourceFile:78)
	at aet.a(SourceFile:444)
	at jr.a(SourceFile:168)
	at adr.a(SourceFile:732)
	at jr.c(SourceFile:105)
	at net.minecraft.server.MinecraftServer.f(SourceFile:230)
	at net.minecraft.server.MinecraftServer.a(SourceFile:200)
	at is.d(SourceFile:182)
	at net.minecraft.server.MinecraftServer.run(SourceFile:315)
	at hi.run(SourceFile:583)

and then it stops the server.