The crash is still occurring even after installing the latest version of the mod.

Just boot Minecraft up with the mod installed, and it crashes.

Here is the crash log:
Description: Mod loading error has occurred

java.lang.Exception: Mod Loading has failed
at net.minecraftforge.fml.CrashReportExtender.dumpModLoadingCrashReport(CrashReportExtender.java:85) [?:?] {re:classloading}
at net.minecraftforge.fml.client.ClientModLoader.completeModLoading(ClientModLoader.java:188) [?:?] {re:classloading,pl:runtimedistcleaner:A}
at net.minecraft.client.Minecraft.lambda$null$1(Minecraft.java:494) [?:?] {re:classloading,pl:accesstransformer:B,pl:runtimedistcleaner:A}
at net.minecraft.client.Minecraft$$Lambda$3948/980751669.run(Unknown Source) [?:?] {}
at net.minecraft.util.Util.func_215077_a(SourceFile:404) [?:?] {re:classloading}
at net.minecraft.client.Minecraft.lambda$new$2(Minecraft.java:490) [?:?] {re:classloading,pl:accesstransformer:B,pl:runtimedistcleaner:A}
at net.minecraft.client.Minecraft$$Lambda$3732/308316550.accept(Unknown Source) [?:?] {}
at net.minecraft.client.gui.ResourceLoadProgressGui.func_230430_a_(ResourceLoadProgressGui.java:113) [?:?] {re:classloading,pl:runtimedistcleaner:A}
at net.minecraft.client.renderer.GameRenderer.func_195458_a(GameRenderer.java:480) [?:?] {re:classloading,pl:accesstransformer:B,pl:runtimedistcleaner:A}
at net.minecraft.client.Minecraft.func_195542_b(Minecraft.java:953) [?:?] {re:classloading,pl:accesstransformer:B,pl:runtimedistcleaner:A}
at net.minecraft.client.Minecraft.func_99999_d(Minecraft.java:584) [?:?] {re:classloading,pl:accesstransformer:B,pl:runtimedistcleaner:A}
at net.minecraft.client.main.Main.main(Main.java:184) [?:?] {re:classloading,pl:runtimedistcleaner:A}
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method) ~[?:1.8.0_51] {}
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62) ~[?:1.8.0_51] {}
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43) ~[?:1.8.0_51] {}
at java.lang.reflect.Method.invoke(Method.java:497) ~[?:1.8.0_51] {}
at net.minecraftforge.fml.loading.FMLClientLaunchProvider.lambda$launchService$0(FMLClientLaunchProvider.java:51) [forge-1.16.3-34.1.32.jar:34.1] {}
at net.minecraftforge.fml.loading.FMLClientLaunchProvider$$Lambda$423/1871312485.call(Unknown Source) [forge-1.16.3-34.1.32.jar:34.1] {}
at cpw.mods.modlauncher.LaunchServiceHandlerDecorator.launch(LaunchServiceHandlerDecorator.java:37) [modlauncher-8.0.5.jar:?] {}
at cpw.mods.modlauncher.LaunchServiceHandler.launch(LaunchServiceHandler.java:54) [modlauncher-8.0.5.jar:?] {}
at cpw.mods.modlauncher.LaunchServiceHandler.launch(LaunchServiceHandler.java:72) [modlauncher-8.0.5.jar:?] {}
at cpw.mods.modlauncher.Launcher.run(Launcher.java:81) [modlauncher-8.0.5.jar:?] {}
at cpw.mods.modlauncher.Launcher.main(Launcher.java:65) [modlauncher-8.0.5.jar:?] {}

A detailed walkthrough of the error, its code path and all known details is as follows:

-- Head --
Thread: Render thread
Stacktrace:
at biomesoplenty.common.biome.BiomeRegistry$RegistrationType.lambda$static$2(BiomeRegistry.java:416) ~[?:?] {re:classloading}
-- MOD biomesoplenty --
Details:
Mod File: BiomesOPlenty-1.16.3-12.0.0.412-universal.jar
Failure message: Biomes O' Plenty (biomesoplenty) encountered an error during the load_registries event phase
java.lang.NoSuchMethodError: net.minecraft.world.biome.Biome.setRegistryName(Ljava/lang/String;)Lnet/minecraftforge/registries/IForgeRegistryEntry;
Mod Version: 1.16.3-12.0.0.410
Mod Issue URL: https://github.com/Glitchfiend/BiomesOPlenty/issues
Exception message: java.lang.NoSuchMethodError: net.minecraft.world.biome.Biome.setRegistryName(Ljava/lang/String;)Lnet/minecraftforge/registries/IForgeRegistryEntry;
Stacktrace:
at biomesoplenty.common.biome.BiomeRegistry$RegistrationType.lambda$static$2(BiomeRegistry.java:416) ~[?:?] {re:classloading}
at biomesoplenty.common.biome.BiomeRegistry$RegistrationType$$Lambda$3429/1684368286.accept(Unknown Source) ~[?:?] {}
at biomesoplenty.common.biome.BiomeRegistry$DeferredRegistration.register(BiomeRegistry.java:677) ~[?:?] {re:classloading}
at biomesoplenty.common.biome.BiomeRegistry.finalizeRegistrations(BiomeRegistry.java:369) ~[?:?] {re:classloading}
at biomesoplenty.init.ModBiomes.registerBiomes(ModBiomes.java:123) ~[?:?] {re:classloading}
at net.minecraftforge.eventbus.ASMEventHandler_5_ModBiomes_registerBiomes_Register.invoke(.dynamic) ~[?:?] {}
at net.minecraftforge.eventbus.ASMEventHandler.invoke(ASMEventHandler.java:85) ~[eventbus-3.0.3-service.jar:?] {}
at net.minecraftforge.eventbus.EventBus.post(EventBus.java:297) ~[eventbus-3.0.3-service.jar:?] {}
at net.minecraftforge.fml.javafmlmod.FMLModContainer.acceptEvent(FMLModContainer.java:120) ~[?:34.1] {re:classloading}
at net.minecraftforge.fml.ModContainer.lambda$buildTransitionHandler$4(ModContainer.java:111) ~[?:?] {re:classloading}
at net.minecraftforge.fml.ModContainer$$Lambda$3060/768795248.run(Unknown Source) ~[?:?] {}
at java.util.concurrent.CompletableFuture$AsyncRun.run(CompletableFuture.java:1618) ~[?:1.8.0_51] {}
at net.minecraftforge.fml.ModWorkManager$SyncExecutor.driveOne(ModWorkManager.java:56) ~[?:?] {re:classloading}
at net.minecraftforge.fml.ModWorkManager$DrivenExecutor.drive(ModWorkManager.java:40) ~[?:?] {re:classloading}
at net.minecraftforge.fml.ModLoader.waitForTransition(ModLoader.java:242) ~[?:?] {re:classloading}
at net.minecraftforge.fml.ModLoader.dispatchAndHandleError(ModLoader.java:229) ~[?:?] {re:classloading}
at net.minecraftforge.fml.ModLoader.gatherAndInitializeMods(ModLoader.java:195) ~[?:?] {re:classloading}
at net.minecraftforge.fml.client.ClientModLoader.lambda$begin$1(ClientModLoader.java:103) ~[?:?] {re:classloading,pl:runtimedistcleaner:A}
at net.minecraftforge.fml.client.ClientModLoader$$Lambda$2876/793808700.run(Unknown Source) ~[?:?] {}
at net.minecraftforge.fml.client.ClientModLoader.lambda$createRunnableWithCatch$4(ClientModLoader.java:123) ~[?:?] {re:classloading,pl:runtimedistcleaner:A}
at net.minecraftforge.fml.client.ClientModLoader$$Lambda$2877/1053832786.run(Unknown Source) ~[?:?] {}
at net.minecraftforge.fml.client.ClientModLoader.begin(ClientModLoader.java:103) ~[?:?] {re:classloading,pl:runtimedistcleaner:A}
at net.minecraft.client.Minecraft.(Minecraft.java:424) [?:?] {re:classloading,pl:accesstransformer:B,pl:runtimedistcleaner:A}
at net.minecraft.client.main.Main.main(Main.java:149) [?:?] {re:classloading,pl:runtimedistcleaner:A}
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method) ~[?:1.8.0_51] {}
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62) ~[?:1.8.0_51] {}
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43) ~[?:1.8.0_51] {}
at java.lang.reflect.Method.invoke(Method.java:497) ~[?:1.8.0_51] {}
at net.minecraftforge.fml.loading.FMLClientLaunchProvider.lambda$launchService$0(FMLClientLaunchProvider.java:51) [forge-1.16.3-34.1.32.jar:34.1] {}
at net.minecraftforge.fml.loading.FMLClientLaunchProvider$$Lambda$423/1871312485.call(Unknown Source) [forge-1.16.3-34.1.32.jar:34.1] {}
at cpw.mods.modlauncher.LaunchServiceHandlerDecorator.launch(LaunchServiceHandlerDecorator.java:37) [modlauncher-8.0.5.jar:?] {}
at cpw.mods.modlauncher.LaunchServiceHandler.launch(LaunchServiceHandler.java:54) [modlauncher-8.0.5.jar:?] {}
at cpw.mods.modlauncher.LaunchServiceHandler.launch(LaunchServiceHandler.java:72) [modlauncher-8.0.5.jar:?] {}
at cpw.mods.modlauncher.Launcher.run(Launcher.java:81) [modlauncher-8.0.5.jar:?] {}
at cpw.mods.modlauncher.Launcher.main(Launcher.java:65) [modlauncher-8.0.5.jar:?] {}

I am using the latest version, which is 1.16.3-12.0.0.412.

You need to update Forge.